Patricia L Hersh

Works (32)

Updated: July 5th, 2023 15:50

2017 journal article

From the weak Bruhat order to crystal posets

MATHEMATISCHE ZEITSCHRIFT, 286(3-4), 1435–1464.

By: P. Hersh n & C. Lenart*

author keywords: Crystal graph; Weak Bruhat order; Key map; Stembridge moves; Order complex
topics (OpenAlex): Advanced Combinatorial Mathematics; Algebraic structures and combinatorial models; Advanced Algebra and Geometry
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Representation Stability for Cohomology of Configuration Spaces in R-d

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2017(5), 1433–1486.

By: P. Hersh n & V. Reiner *

topics (OpenAlex): Homotopy and Cohomology in Algebraic Topology; Algebraic structures and combinatorial models; Advanced Algebra and Geometry
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
4. Quality Education (Web of Science)
5. Gender Equality (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2017 journal article

SB-labelings and posets with each interval homotopy equivalent to a sphere or a ball

JOURNAL OF COMBINATORIAL THEORY SERIES A, 152, 104–120.

By: P. Hersh n & K. Meszaros*

author keywords: Poset topology; Mobius function; Crosscut complex; Tamari lattice; Weak order
topics (OpenAlex): Advanced Algebra and Logic; Advanced Combinatorial Mathematics; Topological and Geometric Data Analysis
TL;DR: It is proved for finite lattices which admit an $SB$-labeling that each open interval has the homotopy type of a ball or of a sphere of some dimension. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2014 journal article

A lexicographic shellability characterization of geometric lattices

JOURNAL OF COMBINATORIAL THEORY SERIES A, 123(1), 8–13.

By: R. Davidson n & P. Hersh n

author keywords: Geometric lattice; Mobius function; Shellability; Order complex
topics (OpenAlex): graph theory and CDMA systems; Advanced Algebra and Logic; Digital Image Processing Techniques
TL;DR: Geometric lattices are characterized in this paper as those finite, atomic lattices such that every atom ordering induces a lexicographic shelling given by an edge labeling known as a minimal labeling. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Regular cell complexes in total positivity

INVENTIONES MATHEMATICAE, 197(1), 57–114.

By: P. Hersh n

topics (OpenAlex): Advanced Combinatorial Mathematics; Homotopy and Cohomology in Algebraic Topology; Commutative Algebra and Its Applications
Source: Web Of Science
Added: August 6, 2018

2014 journal article

The q = -1 phenomenon via homology concentration

Journal of Combinatorics, 5(2), 167–194.

By: P. Hersh n, J. Shareshian* & D. Stanton *

topics (OpenAlex): Advanced Combinatorial Mathematics; Molecular spectroscopy and chirality; Advanced Mathematical Identities
Source: Crossref
Added: July 28, 2019

2013 journal article

Symmetric Chain Decomposition for Cyclic Quotients of Boolean Algebras and Relation to Cyclic Crystals

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2013(2), 463–473.

By: P. Hersh n & A. Schilling *

topics (OpenAlex): Advanced Algebra and Logic; Graph theory and applications; Advanced Combinatorial Mathematics
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Toric cubes

Rendiconti Del Circolo Matematico Di Palermo, 62(1), 67–78.

By: A. Engström *, P. Hersh n & B. Sturmfels *

author keywords: Cube; CW complex; Monomial map; Toric variety; Somialgebraic set
topics (OpenAlex): Advanced Combinatorial Mathematics; Geometric and Algebraic Topology; Commutative Algebra and Its Applications
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
15. Life on Land (Web of Science)
Source: Crossref
Added: June 30, 2019

2011 journal article

Sorting orders, subword complexes, Bruhat order and total positivity

ADVANCES IN APPLIED MATHEMATICS, 46(1-4), 46–53.

By: D. Armstrong* & P. Hersh n

author keywords: Bruhat order; Homotopy type; Quillen Fiber Lemma; Weak order
topics (OpenAlex): Advanced Combinatorial Mathematics; Algebraic structures and combinatorial models; Topological and Geometric Data Analysis
TL;DR: A poset map from a Boolean algebra to the Bruhat order is constructed which unveils an interesting connection between subword complexes, sorting orders, and certain totally nonnegative spaces and gives a simple new proof that the proper part of Bru Hat order is homotopy equivalent to the proper parts of a Booleangebra - that is, to a sphere. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Combinatorial constructions of weight bases: The Gelfand-Tsetlin basis

Electronic Journal of Combinatorics, 17(1).

By: P. Hersh & C. Lenart

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

2010 chapter

Maximum likelihood estimation in latent class models for contingency table data

In P. Gibilisco, E. Riccomagno, M. P. Rogantin, & H. P. Wynn (Eds.), Algebraic and Geometric Methods in Statistics (pp. 27–62).

By: S. Fienberg, P. Hersh*, A. Rinaldo & Y. Zhou *

Ed(s): P. Gibilisco, E. Riccomagno, M. Rogantin & H. Wynn

topics (OpenAlex): Census and Population Estimation; Data-Driven Disease Surveillance; History and advancements in chemistry
Source: Crossref
Added: June 30, 2019

2009 other

A multiplicative deformation of the Möbius function for the poset of partitions of a multiset

By: P. Hersh* & R. Kleinberg

topics (OpenAlex): Advanced Mathematical Identities; Advanced Combinatorial Mathematics; Advanced Mathematical Theories and Applications
TL;DR: A multiplicative deformation is introduced, denoted μ, for the Möbius function of the poset of partitions of a multiset and it is shown that it possesses much more elegant formulas than the usual MöBius function in this case. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

2009 journal article

Random walks on quasisymmetric functions

Advances in Mathematics, 222(3), 782–808.

By: P. Hersh* & S. Hsiao*

author keywords: Quasisymmetric function; Descent algebra; Random walk; Markov chain
topics (OpenAlex): Advanced Combinatorial Mathematics; Mathematical Dynamics and Fractals; Advanced Mathematical Identities
Source: Crossref
Added: June 30, 2019

2009 journal article

Shelling Coxeter-like complexes and sorting on trees

ADVANCES IN MATHEMATICS, 221(3), 812–829.

By: P. Hersh n

author keywords: Shellability; Weak order; Sorting; Coxeter complex; Chessboard complex
topics (OpenAlex): Topological and Geometric Data Analysis; Advanced Combinatorial Mathematics; Markov Chains and Monte Carlo Methods
Source: Web Of Science
Added: August 6, 2018

2009 journal article

The q=-1 phenomenon for bounded (plane) partitions via homology concentration

Discrete Mathematics and Theoretical Computer Science, 471–484.

By: P. Hersh, J. Shareshian & D. Stanton

Source: NC State University Libraries
Added: July 10, 2019

2007 journal article

Chains of Modular Elements and Lattice Connectivity

Order, 23(4), 339–342.

By: P. Hersh* & J. Shareshian

topics (OpenAlex): Advanced Combinatorial Mathematics; Topological and Geometric Data Analysis; Geometric and Algebraic Topology
TL;DR: It is shown that the order complex of any finite lattice with a chain of modular elements is at least (r−2)-connected. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

2007 journal article

Coloring complexes and arrangements

Journal of Algebraic Combinatorics, 27(2), 205–214.

By: P. Hersh* & E. Swartz*

author keywords: convex ear decomposition; chromatic polynomial; coloring complex
topics (OpenAlex): Advanced Combinatorial Mathematics; Graph theory and applications; graph theory and CDMA systems
Source: Crossref
Added: June 30, 2019

2007 journal article

Combinatorics of multigraded Poincaré series for monomial rings

Journal of Algebra, 308(1), 73–90.

By: A. Berglund *, J. Blasiak * & P. Hersh*

author keywords: Poincare series; monomial rings; poset homology; diagonal arrangements
topics (OpenAlex): Commutative Algebra and Its Applications; Advanced Combinatorial Mathematics; Algebraic Geometry and Number Theory
Source: Crossref
Added: June 30, 2019

2005 journal article

Transactions of the American Mathematical Society, 357(02), 509–535.

By: E. Babson* & P. Hersh*

topics (OpenAlex): Topological and Geometric Data Analysis; Rough Sets and Fuzzy Logic; Advanced Combinatorial Mathematics
Source: Crossref
Added: June 30, 2019

2005 chapter

Gröbner basis degree bounds on Tor•^K[Λ](k, k)• and discrete Morse theory for posets

In A. Barvinok, M. Beck, C. Haase, B. Reznick, & V. Welker (Eds.), Integer Points in Polyhedra-geometry, number theory, algebra, optimization (pp. 101–138).

By: P. Hersh & V. Welker

Ed(s): A. Barvinok, M. Beck, C. Haase, B. Reznick & V. Welker

topics (OpenAlex): Topological and Geometric Data Analysis; Advanced Numerical Analysis Techniques; Commutative Algebra and Its Applications
Source: NC State University Libraries
Added: August 18, 2019

2005 journal article

On optimizing discrete Morse functions

Advances in Applied Mathematics, 35(3), 294–322.

By: P. Hersh*

topics (OpenAlex): Topological and Geometric Data Analysis; Homotopy and Cohomology in Algebraic Topology; Advanced Combinatorial Mathematics
TL;DR: Under what conditions may several gradient paths in a discrete Morse function simultaneously be reversed to cancel several pairs of critical cells, to further collapse the complex, and which gradient paths are individually reversible in lexicographic discrete Morse functions on poset order complexes be addressed. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

2004 journal article

A Hodge decomposition for the complex of injective words

Pacific Journal of Mathematics, 214(1), 109–125.

By: P. Hanlon* & P. Hersh*

topics (OpenAlex): Advanced Algebra and Geometry; Advanced Combinatorial Mathematics; Topological and Geometric Data Analysis
Source: Crossref
Added: June 30, 2019

2004 journal article

Connectivity of h-complexes

Journal of Combinatorial Theory, Series A, 105(1), 111–126.

By: P. Hersh*

author keywords: discrete morse function; h-vector; Charney-Davis quantity
topics (OpenAlex): Topological and Geometric Data Analysis; Homotopy and Cohomology in Algebraic Topology; Advanced Combinatorial Mathematics
TL;DR: This paper verifies a conjecture of Edelman and Reiner regarding the homology of the h-complex of a Boolean algebra by constructing a discrete Morse function with no low-dimensional critical cells, implying a lower bound on connectivity. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

2003 journal article

A partitioning and related properties for the quotient complex Δ(Blm)/Sl≀Sm

Journal of Pure and Applied Algebra, 178(3), 255–272.

By: P. Hersh*

topics (OpenAlex): Commutative Algebra and Its Applications; Algebraic structures and combinatorial models; Algebraic Geometry and Number Theory
Source: Crossref
Added: June 30, 2019

2003 journal article

Chain decomposition and the flag f-vector

Journal of Combinatorial Theory, Series A, 103(1), 27–52.

By: P. Hersh*

topics (OpenAlex): Advanced Combinatorial Mathematics; Polynomial and algebraic computation; graph theory and CDMA systems
TL;DR: This work provides formulas for Fp for three classes of locally rank-symmetric posets: graded monoid posets, generalized posets of shuffles and noncrossing partition lattices for classical reflection groups, and flag f-vector expressions for generalized shuffle posets and nonCrossing partitions lattices, which yield symmetric chain decompositions and shellability and supersolvability results. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

2003 journal article

Lexicographic Shellability for Balanced Complexes

Journal of Algebraic Combinatorics, 17(3), 225–254.

By: P. Hersh*

author keywords: shellability; Boolean cell complex; simplicial poset; partition lattice; wreath product
topics (OpenAlex): Advanced Combinatorial Mathematics; Algebraic structures and combinatorial models; Topological and Geometric Data Analysis
Source: Crossref
Added: July 10, 2019

2003 journal article

Multiplicity of the trivial representation in rank-selected homology of the partition lattice

Journal of Algebra, 266(2), 521–538.

By: P. Hanlon* & P. Hersh*

topics (OpenAlex): Algebraic structures and combinatorial models; Advanced Algebra and Geometry; Advanced Combinatorial Mathematics
Source: Crossref
Added: June 30, 2019

2002 journal article

A Short Simplicial h -Vector and the Upper Bound Theorem

Discrete & Computational Geometry, 28(3), 283–289.

By: P. Hersh* & I. Novik*

topics (OpenAlex): Advanced Combinatorial Mathematics; Topological and Geometric Data Analysis; Commutative Algebra and Its Applications
TL;DR: The Upper Bound Conjecture is verified for a class of odd-dimensional simplicial complexes that in particular includes all Eulerian simplicialcomplex with isolated singularities, and relies on a new invariant of simplicial complex—a short simplicial h -vector. (via Semantic Scholar)
Source: Crossref
Added: July 28, 2019

2002 journal article

Two Generalizations of Posets of Shuffles

Journal of Combinatorial Theory, Series A, 97(1), 1–26.

By: P. Hersh*

topics (OpenAlex): Advanced Combinatorial Mathematics; Advanced Mathematical Identities; semigroups and automata theory
TL;DR: A quasi-symmetric function encoding for the flag f-vector, denoted FP, is defined, and this leads to several combinatorial formulas as well as proofs that shuffle posets of multisets are supersolvable and have symmetric chain decompositions. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

1999 thesis

Decomposition and Enumeration in Partially Ordered Sets

(Ph.D. thesis). Massachusetts Institute of Technology.

By: P. Hersh

Source: NC State University Libraries
Added: July 10, 2019

1999 journal article

Deformation of chains via a local symmetric group action

The Electronic Journal of Combinatorics, R27.

By: P. Hersh

Source: NC State University Libraries
Added: July 28, 2019

1999 journal article

On exact n-step domination

Discrete Mathematics, 205(1-3), 235–239.

By: P. Hersh*

topics (OpenAlex): Advanced Graph Theory Research; Limits and Structures in Graph Theory; Complexity and Algorithms in Graphs
TL;DR: It is proved that such subsets of a graph G have order at least ⌊ log 2 n⌋+2 and limit how much better a bound is possible and a related minimization problem for which a lower bound is found. (via Semantic Scholar)
Source: Crossref
Added: June 30, 2019

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