Zobrazeno 1 - 10
of 100
pro vyhledávání: '"Hersh, Patricia"'
Autor:
Gaetz, Christian, Hersh, Patricia
We study the poset topology of lattices arising from orientations of 1-skeleta of directionally simple polytopes, with Bruhat interval polytopes $Q_{e,w}$ as our main example. We show that the order complex $\Delta ((u,v)_w)$ of an interval therein i
Externí odkaz:
http://arxiv.org/abs/2410.08076
Autor:
Hersh, Patricia, Machacek, John
This paper proves that the facet-ridge incidence graph of the order complex of any finite geometric lattice of rank $r$ has diameter at most ${r \choose 2}$. A key ingredient is the well-known fact that every ordering of the atoms of any finite geome
Externí odkaz:
http://arxiv.org/abs/2408.09197
Autor:
Hersh, Patricia, Stadnyk, Grace
Publikováno v:
Combinatorial Theory 4 (1) (2024), 44 pages
Bj\"orner and Wachs introduced CL-shellability as a technique for studying the topological structure of order complexes of partially ordered sets (posets). They also introduced the notion of recursive atom ordering, and they proved that a finite boun
Externí odkaz:
http://arxiv.org/abs/2212.03949
This paper undertakes a study of the structure of the fibers of a family of maps $f_{(i_1,\dots ,i_d)}$ arising from representation theory, motivated both by connections to Lusztig's theory of canonical bases and also by the fact that these fibers en
Externí odkaz:
http://arxiv.org/abs/1903.01420
Autor:
Hersh, Patricia, Kenyon, Richard
Publikováno v:
Advances in Applied Math, 127 (2021), 37 pages
We prove a conjecture of Thomas Lam that the face posets of stratified spaces of planar resistor networks are shellable. These posets are called uncrossing partial orders. This shellability result combines with Lam's previous result that these same p
Externí odkaz:
http://arxiv.org/abs/1803.06217
Autor:
Hersh, Patricia
Given any polytope $P$ and any generic linear functional ${\bf c} $, one obtains a directed graph $G(P,{\bf c})$ from the 1-skeleton of $P$ by orienting each edge $e(u,v)$ from $u$ to $v$ for ${\bf c} (u) < {\bf c} ( v)$. For $P$ a simple polytope an
Externí odkaz:
http://arxiv.org/abs/1802.04342
Autor:
Hersh, Patricia, Kenyon, Richard
Publikováno v:
In Advances in Applied Mathematics June 2021 127
Autor:
Hersh, Patricia, Lenart, Cristian
We investigate the ways in which fundamental properties of the weak Bruhat order on a Weyl group can be lifted (or not) to a corresponding highest weight crystal graph, viewed as a partially ordered set; the latter projects to the weak order via the
Externí odkaz:
http://arxiv.org/abs/1510.05636
Autor:
Hersh, Patricia, Reiner, Victor
This paper studies representation stability in the sense of Church and Farb for representations of the symmetric group $S_n$ on the cohomology of the configuration space of $n$ ordered points in $\mathbf{R}^d$. This cohomology is known to vanish outs
Externí odkaz:
http://arxiv.org/abs/1505.04196
Autor:
Hersh, Patricia
Anders Bjorner characterized which finite graded partially ordered sets arise as the posets of closure relations on cells of a finite, regular CW complex. His characterization of these "CW posets" required each open interval $(\hat{0},u)$ to have ord
Externí odkaz:
http://arxiv.org/abs/1411.1296