Celebrating Loday's associahedron
Abstract We survey Jean-Louis Loday's vertex description of the associahedron, and its far
reaching influence in combinatorics, discrete geometry, and algebra. We present in …
reaching influence in combinatorics, discrete geometry, and algebra. We present in …
Poset edge densities, nearly reduced words, and barely set-valued tableaux
In certain finite posets, the expected down-degree of their elements is the same whether
computed with respect to either the uniform distribution or the distribution weighting an …
computed with respect to either the uniform distribution or the distribution weighting an …
Canonical bases for permutohedral plates
N Early - arxiv preprint arxiv:1712.08520, 2017 - arxiv.org
We study three finite-dimensional quotient vector spaces constructed from the linear span of
the set of characteristic functions of permutohedral cones by imposing two kinds of …
the set of characteristic functions of permutohedral cones by imposing two kinds of …
Commutative algebra of statistical ranking
A model for statistical ranking is a family of probability distributions whose states are
orderings of a fixed finite set of items. We represent the orderings as maximal chains in a …
orderings of a fixed finite set of items. We represent the orderings as maximal chains in a …
Toric matrix Schubert varieties and their polytopes
L Escobar, K Mészáros - Proceedings of the American Mathematical …, 2016 - ams.org
Given a matrix Schubert variety $\overline {X_\pi} $, it can be written as $\overline {X_\pi}=
Y_\pi\times\mathbb {C}^ q $(where $ q $ is maximal possible). We characterize when $ Y …
Y_\pi\times\mathbb {C}^ q $(where $ q $ is maximal possible). We characterize when $ Y …
A quantitative study of pure parallel processes
In this paper, we study the interleaving--or pure merge--operator that most often
characterizes parallelism in concurrency theory. This operator is a principal cause of the so …
characterizes parallelism in concurrency theory. This operator is a principal cause of the so …
[PDF][PDF] P-partitions revisited
arxiv:1106.6235v3 [math.CO] 15 Feb 2012 Page 1 arxiv:1106.6235v3 [math.CO] 15 Feb 2012
P-PARTITIONS REVISITED VALENTIN FÉRAY AND VICTOR REINER Abstract. We compare a …
P-PARTITIONS REVISITED VALENTIN FÉRAY AND VICTOR REINER Abstract. We compare a …
A multivariate hook formula for labelled trees
V Féray, IP Goulden - Journal of Combinatorial Theory, Series A, 2013 - Elsevier
Several hook summation formulae for binary trees have appeared recently in the literature.
In this paper we present an analogous formula for unordered increasing trees of size r …
In this paper we present an analogous formula for unordered increasing trees of size r …
A Toric Analogue for Greene's Rational Function of a Poset
E Catania - arxiv preprint arxiv:2409.04907, 2024 - arxiv.org
Given a finite poset, Greene introduced a rational function obtained by summing certain
rational functions over the linear extensions of the poset. This function has interesting …
rational functions over the linear extensions of the poset. This function has interesting …
Doppelgangers: the Ur-operation and posets of bounded height
In the early 1970's, Richard Stanley and Kenneth Johnson introduced and laid the
groundwork for studying the order polynomial of partially ordered sets (posets). Decades …
groundwork for studying the order polynomial of partially ordered sets (posets). Decades …