Minimal equations for matrix Schubert varieties
Let Matn× n be the space of n× n matrices over a field k; the coordinate ring is R= k [xij] 1≤ i,
j≤ n. Let GLn be the general linear group of invertible n× n matrices with a Borel subgroup B …
j≤ n. Let GLn be the general linear group of invertible n× n matrices with a Borel subgroup B …
The canonical bijection between pipe dreams and bumpless pipe dreams
Y Gao, D Huang - International Mathematics Research Notices, 2023 - academic.oup.com
We present a direct bijection between reduced pipe dreams and reduced bumpless pipe
dreams (BPDs) by interpreting reduced compatible sequences on BPDs and show that this …
dreams (BPDs) by interpreting reduced compatible sequences on BPDs and show that this …
Richardson varieties, projected Richardson varieties and positroid varieties
DE Speyer - arXiv preprint arXiv:2303.04831, 2023 - arxiv.org
This is a survey article on Richardson varieties and their combinatorics. A Richardson
variety is the intersection, inside the flag manifold GL_n/B_+, of a Schubert cell (B_-u …
variety is the intersection, inside the flag manifold GL_n/B_+, of a Schubert cell (B_-u …
Combinatorial commutative algebra rules
A Stelzer, A Yong - arXiv preprint arXiv:2306.00737, 2023 - arxiv.org
arXiv:2306.00737v1 [math.CO] 1 Jun 2023 Page 1 arXiv:2306.00737v1 [math.CO] 1 Jun 2023
COMBINATORIAL COMMUTATIVE ALGEBRA RULES ADA STELZER AND ALEXANDER YONG …
COMBINATORIAL COMMUTATIVE ALGEBRA RULES ADA STELZER AND ALEXANDER YONG …
[PDF][PDF] Schubert geometry and combinatorics
A Woo, A Yong - arXiv preprint arXiv:2303.01436, 2023 - arxiv.org
arXiv:2303.01436v1 [math.AG] 2 Mar 2023 Page 1 arXiv:2303.01436v1 [math.AG] 2 Mar
2023 SCHUBERT GEOMETRY AND COMBINATORICS ALEXANDER WOO AND …
2023 SCHUBERT GEOMETRY AND COMBINATORICS ALEXANDER WOO AND …
Back Stable K-Theory Schubert Calculus
T Lam, SJ Lee, M Shimozono - … Mathematics Research Notices, 2023 - academic.oup.com
We study the back stable-theory Schubert calculus of the infinite flag variety. We define back
stable (double) Grothendieck polynomials and double-Stanley functions and establish …
stable (double) Grothendieck polynomials and double-Stanley functions and establish …
Embedding bumpless pipedreams as Bruhat chains
T Yu - arXiv preprint arXiv:2407.05904, 2024 - arxiv.org
Schubert polynomials are distinguished representatives of Schubert cycles in the
cohomology of the flag variety. In the spirit of Bergeron and Sottile, we use the Bruhat order …
cohomology of the flag variety. In the spirit of Bergeron and Sottile, we use the Bruhat order …
The MatrixSchubert package for Macaulay2
A Almousa, S Grate, D Huang, P Klein… - arXiv preprint arXiv …, 2023 - arxiv.org
We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This
package has tools to construct and study matrix Schubert varieties and alternating sign …
package has tools to construct and study matrix Schubert varieties and alternating sign …
Ladder determinantal varieties and their symbolic blowups
In this article we show that the symbolic Rees algebra of a mixed ladder determinantal ideal
is strongly $ F $-regular. Furthermore, we prove that the symbolic associated graded algebra …
is strongly $ F $-regular. Furthermore, we prove that the symbolic associated graded algebra …
The GeometricDecomposability package for Macaulay2
M Cummings, A Van Tuyl - Journal of Software for Algebra and Geometry, 2024 - msp.org
Using the geometric vertex decomposition property, first defined by Knutson, Miller, and
Yong, a recursive definition for geometrically vertex decomposable ideals was given by …
Yong, a recursive definition for geometrically vertex decomposable ideals was given by …