5 papers
Weak order: Alternating sign matrices, monotone triangles, and bumpless pipe dreams
Laura Escobar, Patricia Klein, Anna Weigandt
In 2018, Hamaker and Reiner introduced weak order for monotone triangles, which extended the usual notion of weak order on the symmetric group. Monotone triangles on $\{1, \ldots,…
Some algebraic properties of ASM varieties
Ilani Axelrod-Freed, Hanson Hao, Matthew Kendall +2
Fulton's matrix Schubert varieties are affine varieties that arise in the study of Schubert calculus in the complete flag variety. Weigandt showed that arbitrary intersections of m…
Algebra and geometry of ASM weak order
Laura Escobar, Patricia Klein, Anna Weigandt
Much of modern Schubert calculus is centered on Schubert varieties in the complete flag variety and on their classes in its integral cohomology ring. Under the Borel isomorphism, t…
Simplicial complexes and matroids with vanishing
Alexandru Constantinescu, Patricia Klein, Thai Thanh Nguyen +2
We investigate quotients by radical monomial ideals for which , the second cotangent cohomology module, vanishes. The dimension of the graded components of , and thus the…
The MatrixSchubert package for Macaulay2
Ayah Almousa, Sean Grate, Daoji Huang +4
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 matr…