Shelling Coxeter-like Complexes and Sorting on Trees (2008)
In their work on `Coxeter-like complexes', Babson and Reiner introduced a simplicial complex $\Delta_T$ associated to each tree $T$ on $n$ nodes, generalizing chessboard complexes and type A Coxeter...
Combinatorial Constructions of Weight Bases: The Gelfand-Tsetlin Basis (2008)
Hersh, Patricia, Lenart, Cristian
This work is part of a project on weight bases for the irreducible representations of semisimple Lie algebras with respect to which the representation matrices of the Chevalley generators are given...
Regular cell complexes in total positivity (2007)
This paper proves a conjecture of Fomin and Shapiro that their combinatorial model for any Bruhat interval is a regular CW complex which is homeomorphic to a ball. The model consists of a stratified...
Random walks on quasisymmetric functions (2007)
Hersh, Patricia, Hsiao, Samuel K.
Conditions are provided under which an endomorphism on quasisymmetric functions gives rise to a left random walk on the descent algebra which is also a lumping of a left random walk on permutations....
Coloring complexes and arrangements (2007)
Steingrimsson's coloring complex and Jonsson's unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class...
Hersh, Patricia, Welker, Volkmar
The purpose of this paper is twofold. 1. We give combinatorial bounds on the ranks of the groups $\Tor^{R}_\bullet(k,k)_\bullet$ in the case where $R = k[\Lambda]$ is an affine semi-group ring, and...
Lexicographic shellability for balanced complexes (2003)
We introduce a notion of lexicographic shellability for pure, balanced boolean cell complexes, modelled after the $CL$-shellability criterion of Bj\"orner and Wachs for posets and its generalization...
Multiplicity of the trivial representation in rank-selected homology of the partition lattice (2003)
We study the multiplicity $b_S(n)$ of the trivial representation in the symmetric group representations $\beta_S$ on the (top) homology of the rank-selected partition lattice $\Pi_n^S$. We break the...
Discrete Morse functions from lexicographic orders (2003)
This paper shows how to construct a discrete Morse function with a relatively small number of critical cells for the order complex of any finite poset with $\hat{0} $ and $\hat{1}$ from any...
A partitioning and related properties for the quotient complex $\Delta (B_{lm})/S_l \wr S_m$ (2003)
We study the quotient complex $\Delta (B_{lm})/S_l\wr S_m$ as a means of deducing facts about the ring $k[x_1,..., x_{lm}]^{S_l\wr S_m}$. It is shown in [He] that this quotient complex is shellable...
A Hodge decomposition for the complex of injective words (2003)
Reiner and Webb compute the $S_n$-module structure for the complex of injective words in [RW]. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper...
On optimizing discrete Morse functions (2003)
Forman introduced discrete Morse theory as a tool for studying CW complexes by essentially collapsing them onto smaller, simpler-to-understand complexes of critical cells in [Fo]. Chari reformulated...
Connectivity of h-complexes (2003)
This paper verifies a conjecture of Edelman and Reiner regarding the homology of the $h$-complex of a Boolean algebra. A discrete Morse function with no low-dimensional critical cells is constructed,...
Chain Decomposition And The Flag F-Vector (2003)
Ehrenborg introduced a quasi-symmetric function encoding, denoted FP , for the ag f-vector of any nite, graded poset P with ^ 0 and ^ 1.
A short simplicial h-vector and the upper bound theorem (2001)
Hersh, Patricia, Novik, Isabella
We verify the Upper Bound Conjecture (UBC) for a class of odd-dimensional simplicial complexes that in particular includes all Eulerian simplicial complexes with isolated singularities. The proof...
Deformation of Chains via a Local Symmetric Group Action (1999)
A symmetric group action on the maximal chains in a finite, ranked poset is local if the adjacent transpositions act in such a way that (i, i + 1) sends each maximal chain either to itself or to one...
Deformation of Chains via a Local Symmetric Group Action (1999)
A symmetric group action on the maximal chains in a finite, ranked poset is local if the adjacent transpositions act in such a way that (i, i + 1) sends each maximal chain either to itself or to one...
We generalize to n steps the notion of exact 2-step domination introduced by Chartrand, et al in [2] and suggest a related minimization problem for which we find a lower bound. A graph G is an exact...