Schubert polynomials as integer point transforms of generalized permutahedra
A Fink, K Mészáros, AS Dizier - Advances in Mathematics, 2018 - Elsevier
We show that the dual character of the flagged Weyl module of any diagram is a positively
weighted integer point transform of a generalized permutahedron. In particular, Schubert …
weighted integer point transform of a generalized permutahedron. In particular, Schubert …
From generalized permutahedra to Grothendieck polynomials via flow polytopes
K Mészáros, A St Dizier - Algebraic Combinatorics, 2020 - numdam.org
We study a family of dissections of flow polytopes arising from the subdivision algebra. To
each dissection of a flow polytope, we associate a polynomial, called the left-degree …
each dissection of a flow polytope, we associate a polynomial, called the left-degree …
On some quadratic algebras I 1/2: combinatorics of Dunkl and Gaudin elements, Schubert, Grothendieck, Fuss-Catalan, universal Tutte and reduced polynomials
AN Kirillov - SIGMA. Symmetry, Integrability and Geometry: Methods …, 2016 - emis.de
On Some Quadratic Algebras I : Combinatorics of Dunkl and Gaudin Elements, Schubert,
Grothendieck, Fuss–Catalan, Universal Tut Page 1 Symmetry, Integrability and Geometry …
Grothendieck, Fuss–Catalan, Universal Tut Page 1 Symmetry, Integrability and Geometry …
Root polytopes, flow polytopes, and order polytopes
K Rietsch, L Williams - arXiv preprint arXiv:2406.15803, 2024 - arxiv.org
In this paper we study the class of polytopes which can be obtained by taking the convex
hull of some subset of the points $\{e_i-e_j\\vert\i\neq j\}\cup\{\pm e_i\} $ in $\mathbb {R}^ n …
hull of some subset of the points $\{e_i-e_j\\vert\i\neq j\}\cup\{\pm e_i\} $ in $\mathbb {R}^ n …
Subword Complexes and Kalai's Conjecture on Reconstruction of Spheres
C Ceballos, J Doolittle - arXiv preprint arXiv:2206.15461, 2022 - arxiv.org
A famous theorem in polytope theory states that the combinatorial type of a simplicial
polytope is completely determined by its facet-ridge graph. This celebrated result was …
polytope is completely determined by its facet-ridge graph. This celebrated result was …
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 …
Flow polytopes with Catalan volumes
S Corteel, JS Kim, K Mészáros - Comptes Rendus. Mathématique, 2017 - numdam.org
We underscore the wealth of flow polytopes with product formulas for volumes. The natural
question arising from our study and previous works [1–3, 8, 10, 11, 13, 14] is: is there a …
question arising from our study and previous works [1–3, 8, 10, 11, 13, 14] is: is there a …
[HTML][HTML] A Hopf algebra of subword complexes
N Bergeron, C Ceballos - Advances in Mathematics, 2017 - Elsevier
We introduce a Hopf algebra structure of subword complexes, including both finite and
infinite types. We present an explicit cancellation free formula for the antipode using acyclic …
infinite types. We present an explicit cancellation free formula for the antipode using acyclic …
Counting integer points of flow polytopes
K Kapoor, K Mészáros, L Setiabrata - Discrete & Computational Geometry, 2021 - Springer
Abstract The Baldoni–Vergne volume and Ehrhart polynomial formulas for flow polytopes
are significant in at least two ways. On one hand, these formulas are in terms of Kostant …
are significant in at least two ways. On one hand, these formulas are in terms of Kostant …
Refinements and Symmetries of the Morris identity for volumes of flow polytopes
AH Morales, W Shi - Comptes Rendus. Mathématique, 2021 - numdam.org
Flow polytopes are an important class of polytopes in combinatorics whose lattice points and
volumes have interesting properties and relations. The Chan–Robbins–Yuen (CRY) …
volumes have interesting properties and relations. The Chan–Robbins–Yuen (CRY) …