Castelnuovo–Mumford regularity of matrix Schubert varieties
O Pechenik, DE Speyer, A Weigandt - Selecta Mathematica, 2024 - Springer
Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete
flag variety. We give a formula for the Castelnuovo–Mumford regularity of matrix Schubert …
flag variety. We give a formula for the Castelnuovo–Mumford regularity of matrix 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 …
The permutahedral variety, mixed Eulerian numbers, and principal specializations of Schubert polynomials
We compute the expansion of the cohomology class of the permutahedral variety in the
basis of Schubert classes. The resulting structure constants are expressed as a sum of …
basis of Schubert classes. The resulting structure constants are expressed as a sum of …
Schubert polynomials, pipe dreams, equivariant classes, and a co-transition formula
A Knutson - Facets of Algebraic Geometry: Volume 2: A Collection …, 2022 - books.google.com
We give a new proof that three families of polynomials coincide: the double Schubert
polynomials of Lascoux and Schutzenberger defined by divided difference operators, the …
polynomials of Lascoux and Schutzenberger defined by divided difference operators, the …
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 …
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 …
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 …
Matrix Schubert varieties, binomial ideals, and reduced Gr\" obner bases
A Stelzer - arXiv preprint arXiv:2306.03006, 2023 - arxiv.org
We prove a sharp lower bound on the number of terms in an element of the reduced Gr\"
obner basis of a Schubert determinantal ideal $ I_w $ under the term order of [Knutson …
obner basis of a Schubert determinantal ideal $ I_w $ under the term order of [Knutson …
Degrees of P-Grothendieck polynomials and regularity of Pfaffian varieties
O Pechenik, MS Denis - arXiv preprint arXiv:2405.17645, 2024 - arxiv.org
We prove a formula for the degrees of Ikeda and Naruse's $ P $-Grothendieck polynomials
using combinatorics of shifted tableaux. We show this formula can be used in conjunction …
using combinatorics of shifted tableaux. We show this formula can be used in conjunction …
Complexity of the usual torus action on Kazhdan-Lusztig varieties
We investigate the class of Kazhdan-Lusztig varieties, and its subclass of matrix Schubert
varieties, endowed with a naturally defined torus action. Writing a matrix Schubert variety …
varieties, endowed with a naturally defined torus action. Writing a matrix Schubert variety …