Works (48)

Updated: April 4th, 2024 06:55

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 journal article

GENERATING FUNCTIONS AND TRIANGULATIONS FOR LECTURE HALL CONES

SIAM JOURNAL ON DISCRETE MATHEMATICS, 30(3), 1470–1479.

author keywords: lecture hall; triangulations; generating functions; Eulerian
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 journal article

The mathematics of lecture hall partitions

JOURNAL OF COMBINATORIAL THEORY SERIES A, 144, 443–475.

By: C. Savage n

author keywords: Theory of partitions; Eulerian polynomials; Ehrhart theory; Lattice point enumeration; Real-rooted polynomials; Gorenstein cones
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)
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
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)
Sources: Crossref, NC State University Libraries
Added: January 19, 2020

2014 journal article

The s-Eulerian polynomials have only real roots

Transactions of the American Mathematical Society, 367(2), 1441–1466.

By: C. Savage n & M. Visontai*

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

2014 journal article

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

RAMANUJAN JOURNAL, 36(1-2), 123–147.

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

author keywords: Lecture hall partition; Polyhedral cone; Generating function; Gorenstein; Self-reciprocal polynomial
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*

Sources: Crossref, NC State University Libraries
Added: February 24, 2020

2012 journal article

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

JOURNAL OF COMBINATORIAL THEORY SERIES A, 119(4), 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
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 journal article

Lattice point generating functions and symmetric cones

JOURNAL OF ALGEBRAIC COMBINATORICS, 38(3), 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
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 journal article

Mahonian pairs

JOURNAL OF COMBINATORIAL THEORY SERIES A, 119(3), 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
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2012 journal article

Rational lecture hall polytopes and inflated Eulerian polynomials

RAMANUJAN JOURNAL, 31(1-2), 97–114.

By: T. Pensyl n & C. Savage n

author keywords: Lecture hall partitions; Eulerian polynomials; Ehrhart theory
UN Sustainable Development Goal Categories
4. Quality Education (Web of Science)
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

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
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)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

2010 journal article

Symmetrically constrained compositions

RAMANUJAN JOURNAL, 23(1-3), 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
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2009 journal article

Minimizing transceivers in optical path networks

JOURNAL OF OPTICAL NETWORKING, 8(5), 454–461.

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

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 journal article

ON q-SERIES IDENTITIES ARISING FROM LECTURE HALL PARTITIONS

INTERNATIONAL JOURNAL OF NUMBER THEORY, 5(2), 327–337.

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

author keywords: Lecture hall partitions; q-analog of Gauss's second theorem
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. (2009, September 6). DISCRETE MATHEMATICS, Vol. 309, pp. 5271–5277.

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

author keywords: Hamilton cycles; Middle levels; Boolean lattice; Necklaces
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2008 journal article

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

JOURNAL OF COMBINATORIAL THEORY SERIES A, 115(6), 967–996.

By: C. Savage n & A. Yee*

author keywords: integer partitions; lecture hall partitions; Euler's partition theorem; Sylvester's bijection; partition bijections
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)
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. (2009, September 6). DISCRETE MATHEMATICS, Vol. 309, pp. 5278–5283.

By: Z. Jiang* & C. Savage*

author keywords: Symmetric chain decompositions; Necklaces; Quotients of the Boolean lattice
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2007 journal article

Complexity of path traffic grooming

JOURNAL OF OPTICAL NETWORKING, 6(11), 1270–1281.

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

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 journal article

The joint distribution of descent and major index over restricted sets of permutations

ANNALS OF COMBINATORICS, 11(3-4), 375–386.

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

author keywords: permutation enumeration; q-Eulerian polynomials; P-partitions
UN Sustainable Development Goal Categories
4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2005 journal article

Common intervals of trees

INFORMATION PROCESSING LETTERS, 93(2), 69–74.

By: S. Heber* & C. Savage*

author keywords: combinatorial problems; algorithms; labeled trees
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 journal article

Pattern avoidance in compositions and multiset permutations

ADVANCES IN APPLIED MATHEMATICS, 36(2), 194–201.

By: C. Savage n & H. Wilf*

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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

Antipodal gray codes

DISCRETE MATHEMATICS, 281(1-3), 221–236.

By: C. Killian n & C. Savage n

author keywords: gray code; Hamiltonian cycle; n-cube
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

Lecture hall theorems, q-series and truncated objects

JOURNAL OF COMBINATORIAL THEORY SERIES A, 108(2), 217–245.

By: S. Corteel & C. Savage*

author keywords: integer partitions; integer compositions; enumeration
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

On the multiplicity of parts in a random composition of a large integer

SIAM JOURNAL ON DISCRETE MATHEMATICS, 18(2), 418–435.

By: P. Hitczenko & C. Savage*

author keywords: compositions of an integer; random compositions; geometric random variables
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)
UN Sustainable Development Goal Categories
4. Quality Education (Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

Partitions and compositions defined by inequalities

RAMANUJAN JOURNAL, 8(3), 357–381.

By: S. Corteel* & C. Savage*

author keywords: integer partitions; integer compositions; enumeration
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2004 journal article

Regularly spaced subsums of integer partitions

ACTA ARITHMETICA, 115(3), 205–216.

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

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)
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

2003 journal article

Anti-lecture hall compositions

Discrete Mathematics, 263(1-3), 275–280.

By: S. Corteel* & C. Savage*

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)
Sources: NC State University Libraries, NC State University Libraries
Added: August 6, 2018

2003 journal article

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

DISCRETE MATHEMATICS, 262(1-3), 241–252.

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

author keywords: Hamiltonian path; gray code; cover graph; augmentation poset
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

2002 journal article

A generating functionology approach to a problem of Wilf

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 142(1), 107–114.

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

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 28). DISCRETE MATHEMATICS, Vol. 249, pp. 31–39.

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

author keywords: integer partitions; lattice paths
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)
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 journal article

On multi-color partitions and the generalized Rogers-Ramanujan identities

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 3(4), 533–548.

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

Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 journal article

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

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 351(1), 379–402.

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

author keywords: Gray code; nonexistence
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1999 journal article

On the multiplicity of parts in a random partition

RANDOM STRUCTURES & ALGORITHMS, 14(2), 185–197.

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

Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 journal article

A bijection for partitions with all ranks at least t

JOURNAL OF COMBINATORIAL THEORY SERIES A, 83(2), 202–220.

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

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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 journal article

A pentagonal number sieve

JOURNAL OF COMBINATORIAL THEORY SERIES A, 82(2), 186–192.

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

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)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 journal article

Basis partitions

DISCRETE MATHEMATICS, 179(1-3), 277–283.

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

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)
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 journal article

Graphical basis partitions

GRAPHS AND COMBINATORICS, 14(3), 241–261.

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

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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1998 journal article

The connectivity of acyclic orientation graphs

DISCRETE MATHEMATICS, 184(1-3), 281–287.

By: C. Savage n & C. Zhang*

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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1997 review

A survey of combinational Gray codes

[Review of ]. SIAM REVIEW, 39(4), 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
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)
Sources: Web Of Science, NC State University Libraries
Added: August 6, 2018

1997 journal article

Efficient generation of graphical partitions

DISCRETE APPLIED MATHEMATICS, 78(1-3), 17–26.

By: T. Barnes n & C. Savage n

author keywords: degree sequences; integer partitions
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)
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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