16 citations · 48 across the 13 of their papers we have counts for
15 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,…
Changing Bases with Pipe Dream Combinatorics
Anna Weigandt
Lascoux and Schützenberger introduced Schubert and Grothendieck polynomials to study the cohomology and K-theory of the complete flag variety. We present explicit combinatorial rul…
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…
An inverse Grassmannian Littlewood-Richardson rule and extensions
Oliver Pechenik, Anna Weigandt
Chow rings of flag varieties have bases of Schubert cycles , indexed by permutations. A major problem of algebraic combinatorics is to give a positive combinatorial formula fo…
Castelnuovo-Mumford regularity of ladder determinantal varieties and patches of Grassmannian Schubert varieties
Jenna Rajchgot, Colleen Robichaux, Anna Weigandt
We give degree formulas for Grothendieck polynomials indexed by vexillary permutations and -avoiding permutations via tableau combinatorics. These formulas generalize a formu…
Castelnuovo-Mumford regularity of matrix Schubert varieties
Oliver Pechenik, David E Speyer, Anna Weigandt
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 Sch…
Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials
Patricia Klein, Anna Weigandt
In their study of infinite flag varieties, Lam, Lee, and Shimozono (2021) introduced bumpless pipe dreams in a new combinatorial formula for double Schubert polynomials. These poly…
Gröbner geometry of Schubert polynomials through ice
Zachary Hamaker, Oliver Pechenik, Anna Weigandt
The geometric naturality of Schubert polynomials and their combinatorial pipe dream representations was established by Knutson and Miller (2005) via antidiagonal Gröbner degenerati…
Bumpless pipe dreams and alternating sign matrices
Anna Weigandt
In their work on the infinite flag variety, Lam, Lee, and Shimozono (2018) introduced objects called bumpless pipe dreams and used them to give a formula for double Schubert polyno…
Degrees of symmetric Grothendieck polynomials and Castelnuovo-Mumford regularity
Jenna Rajchgot, Yi Ren, Colleen Robichaux +2
We give an explicit formula for the degree of the Grothendieck polynomial of a Grassmannian permutation and a closely related formula for the Castelnuovo-Mumford regularity of the…
Derivatives of Schubert polynomials and proof of a determinant conjecture of Stanley
Zachary Hamaker, Oliver Pechenik, David E Speyer +1
We study the action of a differential operator on Schubert polynomials. Using this action, we first give a short new proof of an identity of I. Macdonald (1991). We then prove a de…
Prism tableaux for alternating sign matrix varieties
Anna Weigandt
A prism tableau is a set of reverse semistandard tableaux, each positioned within an ambient grid. Prism tableaux were introduced to provide a formula for the Schubert polynomials…
Schubert polynomials, 132-patterns, and Stanley's conjecture
Anna Weigandt
Motivated by a recent conjecture of R. P. Stanley we offer a lower bound for the sum of the coefficients of a Schubert polynomial in terms of -pattern containment.
Partition Identities and Quiver Representations
Richard Rimanyi, Anna Weigandt, Alexander Yong
We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A.…
The Prism tableau model for Schubert polynomials
Anna Weigandt, Alexander Yong
The Schubert polynomials lift the Schur basis of symmetric polynomials into a basis for Z[x1,x2,...]. We suggest the "prism tableau model" for these polynomials. A novel aspect of…