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).
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).
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)
arxiv.org (repository)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2016 journal article
The mathematics of lecture hall partitions
JOURNAL OF COMBINATORIAL THEORY SERIES A, 144, 443–475.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Crossref, ORCID
Added: January 19, 2020
2015 journal article
The s-Eulerian polynomials have only real roots
Transactions of the American Mathematical Society, 367(2), 1441–1466.
Sources: NC State University Libraries, ORCID
Added: August 6, 2018
2015 journal article
s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones
RAMANUJAN JOURNAL, 36(1-2), 123–147.
author keywords: Lecture hall partition; Polyhedral cone; Generating function; Gorenstein; Self-reciprocal polynomial
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2013 chapter
Hypergeometric Identities Associated with Statistics on Words
In Advances in Combinatorics (pp. 77–100).
Sources: Crossref, ORCID
Added: February 24, 2020
2013 journal article
Lattice point generating functions and symmetric cones
JOURNAL OF ALGEBRAIC COMBINATORICS, 38(3), 543–566.
author keywords: Lattice point generating function; Polyhedral cone; Finite reflection group; Coxeter group; Symmetrically constrained composition; Permutation statistics; Lecture hall partition
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2013 journal article
Rational lecture hall polytopes and inflated Eulerian polynomials
RAMANUJAN JOURNAL, 31(1-2), 97–114.
author keywords: Lecture hall partitions; Eulerian polynomials; Ehrhart theory
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2012 journal article
Mahonian pairs
JOURNAL OF COMBINATORIAL THEORY SERIES A, 119(3), 526–545.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2012 journal article
The 1/k-Eulerian polynomials
Electronic Journal of Combinatorics, 19(1).
Source: NC State University Libraries
Added: August 6, 2018
2011 journal article
On an identity of Gessel and Stanton and the new little Göllnitz identities
Advances in Applied Mathematics, 46(1-4), 563–575.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Crossref, ORCID
Added: August 28, 2020
2010 journal article
Symmetrically constrained compositions
RAMANUJAN JOURNAL, 23(1-3), 355–369.
author keywords: Symmetrically constrained composition; Partition analysis; Permutation statistics; Generating function; Lattice-point enumeration
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2009 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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2009 journal article
Minimizing transceivers in optical path networks
JOURNAL OF OPTICAL NETWORKING, 8(5), 454–461.
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, ORCID
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.
author keywords: Lecture hall partitions; q-analog of Gauss's second theorem
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2009 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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2007 journal article
Complexity of path traffic grooming
JOURNAL OF OPTICAL NETWORKING, 6(11), 1270–1281.
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, ORCID
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.
author keywords: permutation enumeration; q-Eulerian polynomials; P-partitions
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2006 journal article
Pattern avoidance in compositions and multiset permutations
ADVANCES IN APPLIED MATHEMATICS, 36(2), 194–201.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2005 journal article
Common intervals of trees
INFORMATION PROCESSING LETTERS, 93(2), 69–74.
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, ORCID
Added: August 6, 2018
2004 journal article
Antipodal gray codes
DISCRETE MATHEMATICS, 281(1-3), 221–236.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
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.
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, ORCID
Added: August 6, 2018
2004 journal article
Partitions and compositions defined by inequalities
RAMANUJAN JOURNAL, 8(3), 357–381.
author keywords: integer partitions; integer compositions; enumeration
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2004 journal article
Regularly spaced subsums of integer partitions
ACTA ARITHMETICA, 115(3), 205–216.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2004 journal article
Venn diagrams and symmetric chain decompositions in the Boolean lattice
Electronic Journal of Combinatorics, 11(1).
Source: NC State University Libraries
Added: August 6, 2018
2003 journal article
Anti-lecture hall compositions
Discrete Mathematics, 263(1-3), 275–280.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: NC State University Libraries, ORCID
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
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.
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
2002 journal article
On the number of graphical forest partitions
Ars Combinatoria, 65(2002 Oct), 33–37.
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.
Sources: Web Of Science, ORCID
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.
author keywords: Gray code; nonexistence
Sources: Web Of Science, ORCID
Added: August 6, 2018
1999 journal article
On the multiplicity of parts in a random partition
RANDOM STRUCTURES & ALGORITHMS, 14(2), 185–197.
Sources: Web Of Science, ORCID
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.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 journal article
A pentagonal number sieve
JOURNAL OF COMBINATORIAL THEORY SERIES A, 82(2), 186–192.
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
9. Industry, Innovation and Infrastructure
(Web of Science)
15. Life on Land
(OpenAlex)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 journal article
Basis partitions
DISCRETE MATHEMATICS, 179(1-3), 277–283.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 journal article
Durfee polynomials
Electronic Journal of Combinatorics, 5(1, Research paper 32), 1–21.
Source: NC State University Libraries
Added: August 6, 2018
1998 journal article
Graphical basis partitions
GRAPHS AND COMBINATORICS, 14(3), 241–261.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1998 journal article
The connectivity of acyclic orientation graphs
DISCRETE MATHEMATICS, 184(1-3), 281–287.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1997 review
A survey of combinational Gray codes
[Review of ]. SIAM REVIEW, 39(4), 605–629.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
Added: August 6, 2018
1997 journal article
Efficient generation of graphical partitions
DISCRETE APPLIED MATHEMATICS, 78(1-3), 17–26.
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)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID
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).
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.
Source: NC State University Libraries
Added: August 6, 2018
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