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)

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.

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, 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.

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, 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.

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.

UN Sustainable Development Goal Categories

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).

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.

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, 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.

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

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, 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.

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).

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.

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, NC State University Libraries

Added: August 28, 2020

2010 journal article

Symmetrically constrained compositions

*RAMANUJAN JOURNAL*, *23*(1-3), 355–369.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

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.

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.

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, 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.

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, 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.

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, 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.

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, NC State University Libraries

Added: August 6, 2018

2007 journal article

Complexity of path traffic grooming

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

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.

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.

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.

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

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, 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.

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, 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.

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.

author keywords: integer partitions; integer compositions; enumeration

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

Regularly spaced subsums of integer partitions

*ACTA ARITHMETICA*, *115*(3), 205–216.

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

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.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

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.

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, 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.

UN Sustainable Development Goal Categories

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 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, 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.

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, 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.

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.

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.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

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.

UN Sustainable Development Goal Categories

9. Industry, Innovation and Infrastructure
(Web of Science)

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.

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

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.

Source: NC State University Libraries

Added: August 6, 2018

1998 journal article

Graphical basis partitions

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

UN Sustainable Development Goal Categories

4. Quality Education
(Web of Science)

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.

UN Sustainable Development Goal Categories

11. Sustainable Cities and Communities
(Web of Science)

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.

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, NC State University Libraries

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, 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).

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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