Carla Diane Savage

Works (48)

Updated: February 10th, 2025 14:29

2018 journal article

Lecture hall partitions and the affine hyperoctahedral group

Electronic Journal of Combinatorics, 25(1).

By: C. Hanusa & C. Savage 

Source: NC State University Libraries
Added: August 6, 2018

2018 journal article

Patterns in inversion sequences II: Inversion sequences avoiding triples of relations

Journal of Integer Sequences, 21(2).

By: M. Martinez & C. Savage 

Source: NC State University Libraries
Added: August 6, 2018

2016 article

Generating Functions and Triangulations for Lecture Hall Cones

Beck, M., Braun, B., Köppe, M., Savage, C. D., & Zafeirakopoulos, Z. (2016, January 1). SIAM Journal on Discrete Mathematics, Vol. 30, pp. 1470–1479.

By: M. Beck  n, B. Braun  n, M. Köppe  n, C. Savage n  & Z. Zafeirakopoulos  n

author keywords: lecture hall; triangulations; generating functions; Eulerian
topics (OpenAlex): Advanced Combinatorial Mathematics; Algebraic structures and combinatorial models; Advanced Topics in Algebra
TL;DR: The Hilbert basis for the lecture hall cone of L_n is described and observations and a conjecture regarding the structure of unimodular triangulations of $L_n$ are concluded, including connections between enumerative and algebraic properties of the cone and cones over unit cubes. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2016 article

The mathematics of lecture hall partitions

Savage, C. D. (2016, July 17). Journal of Combinatorial Theory Series A, Vol. 144, pp. 443–475.

By: C. Savage n 

author keywords: Theory of partitions; Eulerian polynomials; Ehrhart theory; Lattice point enumeration; Real-rooted polynomials; Gorenstein cones
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Commutative Algebra and Its Applications
TL;DR: An overview of some of the surprising connections that have surfaced in the process of trying to understand the lecture hall partitions is given. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2015 journal article

Anti-lecture hall compositions and Andrews' generalization of the Watson–Whipple transformation

Journal of Combinatorial Theory, Series A, 134, 188–195.

By: S. Corteel *, J. Lovejoy* & C. Savage n 

author keywords: Lecture hall partitions; Andrews' transformation; Watson-Whipple transformation
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; semigroups and automata theory
TL;DR: A three-variable generating function is found for the set of sequences satisfying k and the main tools are elementary combinatorics and Andrews' generalization of the Watson-Whipple transformation. (via Semantic Scholar)
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Sources: Crossref, NC State University Libraries
Added: January 19, 2020

2014 article

The [?]-Eulerian polynomials have only real roots

Savage, C., & Visontai, M. (2014, October 10). Transactions of the American Mathematical Society, Vol. 367, pp. 1441–1466.

By: C. Savage n  & M. Visontai*

topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; semigroups and automata theory
Sources: NC State University Libraries, NC State University Libraries
Added: August 6, 2018

2014 article

s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones

Beck, M., Braun, B., Köppe, M., Savage, C. D., & Zafeirakopoulos, Z. (2014, January 13). The Ramanujan Journal, Vol. 36, pp. 123–147.

By: M. Beck*, B. Braun*, M. Köppe*, C. Savage n  & Z. Zafeirakopoulos*

author keywords: Lecture hall partition; Polyhedral cone; Generating function; Gorenstein; Self-reciprocal polynomial
topics (OpenAlex): Advanced Combinatorial Mathematics; Algebraic structures and combinatorial models; Commutative Algebra and Its Applications; Advanced Mathematical Identities; Mathematical functions and polynomials
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2013 chapter

Hypergeometric Identities Associated with Statistics on Words

In Advances in Combinatorics (pp. 77–100).

By: G. Andrews *, C. Savage n  & H. Wilf*

topics (OpenAlex): Data Management and Algorithms; Advanced Combinatorial Mathematics; Data Visualization and Analytics
Sources: Crossref, NC State University Libraries
Added: February 24, 2020

2012 article

Ehrhart series of lecture hall polytopes and Eulerian polynomials for inversion sequences

Savage, C. D., & Schuster, M. J. (2012, January 7). Journal of Combinatorial Theory Series A, Vol. 119, pp. 850–870.

By: C. Savage n  & M. Schuster n

author keywords: Lecture hall partitions; Eulerian polynomials; Permutation statistics; Ehrhart-theory; Inversion sequences; q-Series identities
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities
TL;DR: This work uses Ehrhart theory to relate the partition theory of lecture hall partitions to their geometry and shows how four different statistics are related through the three s-families of partitions, polytopes, and inversion sequences. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 article

Lattice point generating functions and symmetric cones

Beck, M., Bliem, T., Braun, B., & Savage, C. D. (2012, November 29). Journal of Algebraic Combinatorics, Vol. 38, pp. 543–566.

By: M. Beck *, T. Bliem, B. Braun * & C. Savage n 

author keywords: Lattice point generating function; Polyhedral cone; Finite reflection group; Coxeter group; Symmetrically constrained composition; Permutation statistics; Lecture hall partition
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Bayesian Methods and Mixture Models
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 article

Rational lecture hall polytopes and inflated Eulerian polynomials

Pensyl, T. W., & Savage, C. D. (2012, September 5). The Ramanujan Journal, Vol. 31, pp. 97–114.

By: T. Pensyl n & C. Savage n 

author keywords: Lecture hall partitions; Eulerian polynomials; Ehrhart theory
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Mathematical Dynamics and Fractals
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 journal article

The 1/k-Eulerian polynomials

Electronic Journal of Combinatorics, 19(1).

By: C. Savage  & G. Viswanathan

Source: NC State University Libraries
Added: August 6, 2018

2011 article

Mahonian pairs

Sagan, B. E., & Savage, C. D. (2011, November 19). Journal of Combinatorial Theory Series A, Vol. 119, pp. 526–545.

By: B. Sagan & C. Savage* 

author keywords: Ballot sequence; Greene-Kleitman symmetric chain decomposition; Foata's fundamental bijection; Integer partition; Inversion number; Mahonian statistic; Major index; Rank of a partition; q-Catalan number; q-Fibonacci number
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; semigroups and automata theory
TL;DR: The definition of Mahonian pairs is generalized to infinite sets and used as a tool to connect a partition bijection of Corteel-Savage-Venkatraman with the Greene-Kleitman decomposition of a Boolean algebra into symmetric chains. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2010 journal article

On an identity of Gessel and Stanton and the new little Göllnitz identities

Advances in Applied Mathematics, 46(1-4), 563–575.

By: C. Savage*  & A. Sills *

author keywords: Integer partitions; q-Series identities; q-Gauss summation; Little Gollnitz partition theorems; Gollnitz-Gordon partition theorem; Lebesgue identity
topics (OpenAlex): Advanced Mathematical Identities; Advanced Combinatorial Mathematics; Mathematical functions and polynomials
TL;DR: It is shown that an identity of Gessel and Stanton can be viewed as a symmetric version of a recent analytic variation of the little Gollnitz identities, and a refinement of the Gessel-Stanton identity is derived that suggests a similar interpretation is possible. (via Semantic Scholar)
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Sources: Crossref, NC State University Libraries
Added: August 28, 2020

2010 article

Symmetrically constrained compositions

Beck, M., Gessel, I. M., Lee, S., & Savage, C. D. (2010, April 21). The Ramanujan Journal, Vol. 23, pp. 355–369.

By: M. Beck *, I. Gessel *, S. Lee  n & C. Savage n 

author keywords: Symmetrically constrained composition; Partition analysis; Permutation statistics; Generating function; Lattice-point enumeration
topics (OpenAlex): Advanced Combinatorial Mathematics; Bayesian Methods and Mixture Models; Advanced Mathematical Identities
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2009 article

Minimizing transceivers in optical path networks

Iyer, P., Dutta, R., & Savage, C. D. (2009, April 8). Journal of Optical Networking, Vol. 8, pp. 454–461.

By: P. Iyer n, R. Dutta n  & C. Savage n 

topics (OpenAlex): Advanced Optical Network Technologies; Optical Network Technologies; Software-Defined Networks and 5G
TL;DR: The traffic grooming problem in unidirectional, WDM path networks is considered with the goal of minimizing the number of transceivers and it is conclusively shown that the problem is NP-hard, even under the restriction of the egress traffic model. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2009 article

ON q-SERIES IDENTITIES ARISING FROM LECTURE HALL PARTITIONS

ANDREWS, G. E. O. R. G. E. E., CORTEEL, S. Y. L. V. I. E., & SAVAGE, C. A. R. L. A. D. (2009, March 1). International Journal of Number Theory, Vol. 5, pp. 327–337.

By: G. Andrews *, S. Corteel * & C. Savage n 

author keywords: Lecture hall partitions; q-analog of Gauss's second theorem
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Advanced Mathematical Theories and Applications
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2008 article

An update on the middle levels problem

Shields, I., Shields, B. J., & Savage, C. D. (2008, February 22). Discrete Mathematics, Vol. 306, pp. 5271–5277.

By: I. Shields*, B. Shields * & C. Savage n 

author keywords: Hamilton cycles; Middle levels; Boolean lattice; Necklaces
topics (OpenAlex): graph theory and CDMA systems; Advanced Graph Theory Research; Limits and Structures in Graph Theory
TL;DR: The result was achieved by an algorithmic improvement that made it possible to find a Hamilton path in a reduced graph having 129,644,790 vertices, using a 64-bit personal computer. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2008 article

Euler's partition theorem and the combinatorics of ℓ-sequences

Savage, C. D., & Yee, A. J. (2008, February 20). Journal of Combinatorial Theory Series A, Vol. 115, pp. 967–996.

By: C. Savage n  & A. Yee *

author keywords: integer partitions; lecture hall partitions; Euler's partition theorem; Sylvester's bijection; partition bijections
topics (OpenAlex): Advanced Mathematical Identities; Analytic Number Theory Research; Advanced Combinatorial Mathematics
TL;DR: A surprisingly simple bijection is provided for Euler's partition theorem, which involves a family of partitions constrained by the ratio of successive parts, and the intrinsic role played by the combinatorics of @?-sequences is uncovered. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2008 article

On the existence of symmetric chain decompositions in a quotient of the Boolean lattice

Jiang, Z., & Savage, C. D. (2008, January 7). Discrete Mathematics, Vol. 306, pp. 5278–5283.

By: Z. Jiang* & C. Savage* 

author keywords: Symmetric chain decompositions; Necklaces; Quotients of the Boolean lattice
topics (OpenAlex): Advanced Combinatorial Mathematics; graph theory and CDMA systems; semigroups and automata theory
TL;DR: In this note it is described how it suffices to focus on subposets induced by necklaces with periodic block codes, substantially reducing the size of the problem. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2007 article

Complexity of path traffic grooming

Iyer, P., Dutta, R., & Savage, C. D. (2007, January 1). Journal of Optical Networking, Vol. 6, pp. 1270–1281.

By: P. Iyer n, R. Dutta n  & C. Savage n 

topics (OpenAlex): Advanced Optical Network Technologies; Optical Network Technologies; Photonic and Optical Devices
TL;DR: The borderline between tractability and intractability is explored by considering grooming in unidirectional path networks in which all traffic requests are destined for a single egress node and it is shown that at least the problem of routing traffic on a given virtual topology to minimize electronic switching becomes polynomial on the egress model. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2007 article

The Joint Distribution of Descent and Major Index over Restricted Sets of Permutations

Corteel, S., Gessel, I. M., Savage, C. D., & Wilf, H. S. (2007, December 1). Annals of Combinatorics, Vol. 11, pp. 375–386.

By: S. Corteel *, I. Gessel *, C. Savage n  & H. Wilf*

author keywords: permutation enumeration; q-Eulerian polynomials; P-partitions
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; semigroups and automata theory
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2005 article

Common intervals of trees

Heber, S., & Savage, C. D. (2005, January 1). Information Processing Letters, Vol. 93, pp. 69–74.

By: S. Heber*  & C. Savage* 

author keywords: combinatorial problems; algorithms; labeled trees
topics (OpenAlex): Advanced Graph Theory Research; Constraint Satisfaction and Optimization; semigroups and automata theory
TL;DR: This paper considers the problem of finding common intervals of trees, a generalization of the concept of common intervals in permutations, and proposes some genetic algorithms using subtour exchange crossover based on common intervals. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2005 article

Pattern avoidance in compositions and multiset permutations

Savage, C. D., & Wilf, H. S. (2005, December 23). Advances in Applied Mathematics, Vol. 36, pp. 194–201.

By: C. Savage n  & H. Wilf*

topics (OpenAlex): semigroups and automata theory; Advanced Combinatorial Mathematics; Advanced Algebra and Logic
TL;DR: A bijective proof of the fact that if M=1^a^"^1...k^a ^"^k is a given multiset then the number of permutations of M that avoid the pattern (123) is a symmetric function of the multiplicities a"1,...,a"k. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 article

Antipodal Gray codes

Killian, C. E., & Savage, C. D. (2004, February 11). Discrete Mathematics, Vol. 281, pp. 221–236.

By: C. Killian n & C. Savage n 

author keywords: gray code; Hamiltonian cycle; n-cube
topics (OpenAlex): Algorithms and Data Compression; Coding theory and cryptography; Cellular Automata and Applications
TL;DR: This paper provides a recursive construction to prove existence of n antipodal Gray codes when n is a power of 2, and shows they are not possible for odd n>3 or for n=6. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 article

Lecture hall theorems, q-series and truncated objects

Corteel, S., & Savage, C. D. (2004, October 13). Journal of Combinatorial Theory Series A, Vol. 108, pp. 217–245.

By: S. Corteel & C. Savage* 

author keywords: integer partitions; integer compositions; enumeration
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Mathematical functions and polynomials
TL;DR: It is shown here that the refined theorems for both lecture hall partitions and anti-lecture hall compositions can be obtained as straightforward consequences of two q-Chu Vandermonde identities, once an appropriate recurrence is derived. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 article

On the Multiplicity of Parts in a Random Composition of a Large Integer

Hitczenko, P., & Savage, C. D. (2004, January 1). SIAM Journal on Discrete Mathematics, Vol. 18, pp. 418–435.

By: P. Hitczenko & C. Savage* 

author keywords: compositions of an integer; random compositions; geometric random variables
topics (OpenAlex): Analytic Number Theory Research; Limits and Structures in Graph Theory; Advanced Mathematical Identities
TL;DR: A more careful analysis uncovers an unexpected result: $(\ln n)\P(A_n^{(m)})$ does not have a limit but instead oscillates around the value $1/m$ as $n\to\infty$. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 article

Partitions and Compositions Defined by Inequalities

Corteel, S., & Savage, C. D. (2004, September 1). The Ramanujan Journal, Vol. 8, pp. 357–381.

By: S. Corteel * & C. Savage* 

author keywords: integer partitions; integer compositions; enumeration
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Functional Equations Stability Results
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

Venn diagrams and symmetric chain decompositions in the Boolean lattice

Electronic Journal of Combinatorics, 11(1).

By: J. Griggs, C. Killian & C. Savage 

Source: NC State University Libraries
Added: August 6, 2018

2004 article

\tRegularly Spaced Subsums of Integer Partitions

Canfield, E. R., Savage, C. D., & Wilf, H. S. (2003, January 1). Acta Arithmetica, Vol. 115, pp. 205–216.

By: E. Canfield*, C. Savage n  & H. Wilf*

topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Advanced Mathematical Theories and Applications; Analytic Number Theory Research; Sports Dynamics and Biomechanics
TL;DR: The methods used involve asymptotic formulas for the behavior of Lambert series and the Zeta function of Hurwitz and it is shown that if f(n,j)$ is the number of partitions of $n$ the sum of whose parts of even index is $j, then for every $n,f agrees with a certain universal sequence, Sloane's sequence. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2003 article

Anti-Lecture Hall Compositions

Corteel, S., & Savage, C. D. (2003, February 1). Discrete Mathematics, Vol. 263, pp. 275–280.

By: S. Corteel * & C. Savage* 

topics (OpenAlex): Advanced Mathematical Identities; Advanced Combinatorial Mathematics; Analytic Number Theory Research
TL;DR: It is shown that the generating function of the set Ak of integer sequences is Σλ ∈ Ak q|λ| = Πi=1k (1 + qi)/(1 - q i+1), where |λ | = λ1 +...+ λk. (via Semantic Scholar)
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Sources: NC State University Libraries, NC State University Libraries
Added: August 6, 2018

2003 article

On the existence of Hamiltonian paths in the cover graph of M(n)

Savage, C. D., Shields, I., & West, D. B. (2003, January 17). Discrete Mathematics, Vol. 262, pp. 241–252.

By: C. Savage n , I. Shields* & D. West *

author keywords: Hamiltonian path; gray code; cover graph; augmentation poset
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; graph theory and CDMA systems
TL;DR: It is shown that the cover graph of M(n) has a Hamiltonian path if and only if(n+12) is odd and n ≠ 5. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2002 article

A generating functionology approach to a problem of Wilf

Hitczenko, P., Rousseau, C., & Savage, C. D. (2002, May 1). Journal of Computational and Applied Mathematics, Vol. 142, pp. 107–114.

By: P. Hitczenko *, C. Rousseau* & C. Savage n 

topics (OpenAlex): Advanced Mathematical Identities; Analytic Number Theory Research; Advanced Combinatorial Mathematics
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2002 article

A lattice path approach to counting partitions with minimum rank t

Burstein, A., Corteel, S., Postnikov, A., & Savage, C. D. (2002, April 1). Discrete Mathematics, Vol. 249, pp. 31–39.

By: A. Burstein *, S. Corteel, A. Postnikov* & C. Savage n 

author keywords: integer partitions; lattice paths
topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Analytic Number Theory Research
TL;DR: A combinatorial proof via lattice paths of the following result due to Andrews and Bressoud: for t≤1, the number of partitions of n with all successive ranks at least t is equal to the number that has no part of size 2 - t. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2002 journal article

On the number of graphical forest partitions

Ars Combinatoria, 65(2002 Oct), 33–37.

By: D. Frank, C. Savage  & J. Sellers

Source: NC State University Libraries
Added: August 6, 2018

2001 article

ON MULTI-COLOR PARTITIONS AND THE GENERALIZED ROGERS–RAMANUJAN IDENTITIES

JING, N. A. I. H. U. A. N., MISRA, K. A. I. L. A. S. H. C., & SAVAGE, C. A. R. L. A. D. (2001, November 1). Communications in Contemporary Mathematics, Vol. 3, pp. 533–548.

By: N. Jing n , K. Misra n & C. Savage n 

topics (OpenAlex): Advanced Mathematical Identities; Advanced Combinatorial Mathematics; Analytic Number Theory Research
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 article

Combinatorial families that are exponentially far from being listable in Gray code sequence

Chinburg, T., Savage, C., & Wilf, H. (1999, January 1). Transactions of the American Mathematical Society, Vol. 351, pp. 379–402.

By: T. Chinburg *, C. Savage n  & H. Wilf*

author keywords: Gray code; nonexistence
topics (OpenAlex): Algorithms and Data Compression; semigroups and automata theory; Advanced Combinatorial Mathematics
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 article

On the multiplicity of parts in a random partition

Corteel, S., Pittel, B., Savage, C. D., & Wilf, H. S. (1999, March 1). Random Structures and Algorithms, Vol. 14, pp. 185–197.

By: S. Corteel *, B. Pittel *, C. Savage n  & H. Wilf*

topics (OpenAlex): Analytic Number Theory Research; Advanced Mathematical Identities; Advanced Combinatorial Mathematics
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 article

A Bijection for Partitions with All Ranks at Least t

Corteel, S., Savage, C. D., & Venkatraman, R. (1998, August 1). Journal of Combinatorial Theory Series A, Vol. 83, pp. 202–220.

By: S. Corteel *, C. Savage n  & R. Venkatraman n

topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; Analytic Number Theory Research
TL;DR: A simple bijection is given for this identity which generalizes a result of Cheema and Gordon for 2-rowed plane partitions and gives an interpretation of the difference of (shifted) successive Gaussian polynomials which it relates to other interpretations of Andrews and Fishel. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 article

A Pentagonal Number Sieve

Corteel, S., Savage, C. D., Wilf, H. S., & Zeilberger, D. (1998, May 1). Journal of Combinatorial Theory Series A, Vol. 82, pp. 186–192.

By: S. Corteel  n, C. Savage n , H. Wilf* & D. Zeilberger*

topics (OpenAlex): Advanced Combinatorial Mathematics; Analytic Number Theory Research; Advanced Mathematical Identities
TL;DR: A general “pentagonal sieve” theorem is proved that has corollaries such as the following: iff,gare two monic polynomials of the same degree over the fieldGF(q), then the probability thatf,Gare relatively prime is 1?1/q. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 article

Basis partitions

Nolan, J. M., Savage, C. D., & Wilf, H. S. (1998, January 1). Discrete Mathematics, Vol. 179, pp. 277–283.

By: J. Nolan n, C. Savage n  & H. Wilf*

topics (OpenAlex): Advanced Mathematical Identities; Advanced Combinatorial Mathematics; Mathematical functions and polynomials
TL;DR: For this family of partitions, a recurrence, a generating function, identities relating basis partitions to more familiar families of partition, and a new characterization of basis partitions are given. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 journal article

Durfee polynomials

Electronic Journal of Combinatorics, 5(1, Research paper 32), 1–21.

By: E. Canfield, S. Corteel & C. Savage 

Source: NC State University Libraries
Added: August 6, 2018

1998 article

Graphical Basis Partitions

Nolan, J. M., Sivaraman, V., Savage, C. D., & Tiwari, P. K. (1998, August 31). Graphs and Combinatorics, Vol. 14, pp. 241–261.

By: J. Nolan n, V. Sivaraman n, C. Savage n  & P. Tiwari n

topics (OpenAlex): Digital Image Processing Techniques; Topological and Geometric Data Analysis; Graph theory and applications
TL;DR: Empirical evidence is given which leads to conjecture that, as n approaches infinity, the fraction of basis partitions of n which are graphical approaches the same limit as the fraction that is the degree sequence of a simple, undirected graph. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 article

The connectivity of acyclic orientation graphs

Savage, C. D., & Zhang, C.-Q. (1998, April 1). Discrete Mathematics, Vol. 184, pp. 281–287.

By: C. Savage n  & C. Zhang *

topics (OpenAlex): Advanced Graph Theory Research; Interconnection Networks and Systems; graph theory and CDMA systems
TL;DR: A simple graph-theoretic proof that if H is a triangle-free graph with minimum degree at least k, and the graph obtained by contracting the edges of a matching in H is k-connected, then H isk-connected. (via Semantic Scholar)
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Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1997 article

A Survey of Combinatorial Gray Codes

Savage, C. (1997, January 1). SIAM Review, Vol. 39, pp. 605–629.

By: C. Savage* 

author keywords: Gray codes; Hamilton cycles; acyclic orientations; binary strings; Boolean lattice; Catalan families; Cayley graphs; combinations; compositions; de Bruijn sequences; integer partitions; linear extensions; necklaces; permutations; restricted growth functions; set partitions; vertex-transitive graphs
topics (OpenAlex): Advanced Combinatorial Mathematics; graph theory and CDMA systems; Cellular Automata and Applications
TL;DR: The area of combinatorial Gray codes is surveyed, recent results, variations, and trends are described, and some open problems are highlighted. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1997 article

Efficient generation of graphical partitions

Barnes, T. M., & Savage, C. D. (1997, October 1). Discrete Applied Mathematics, Vol. 78, pp. 17–26.

By: T. Barnes n & C. Savage n 

author keywords: degree sequences; integer partitions
topics (OpenAlex): Digital Image Processing Techniques; Topological and Geometric Data Analysis; Digital Filter Design and Implementation
TL;DR: This is the first algorithm shown to achieve such efficiency for generating G(n), and the direct approach differs from earlier ‘generate and reject’ schemes and the ‘interval/gap’ approach. (via Semantic Scholar)
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4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

chapter

A Note on the complexity of converter placement supporting broadcast in WDM optical networks

Dutta, R., & Savage, C. In 2005 International Conference on Telecommunication Systems, Modeling and Analysis (pp. 23–31).

By: R. Dutta  & C. Savage 

Source: NC State University Libraries
Added: August 6, 2018

chapter

On the complexity of path traffic grooming.

Iyer, P., Dutta, R., & Savage, C. D. In Proceedings of the Second International IEEE/Create-net workshop on traffic grooming (pp. 295–301). Los Alamitos, CA: IEEE Computer Society.

By: P. Iyer, R. Dutta  & C. Savage 

Source: NC State University Libraries
Added: August 6, 2018

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