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,…
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…
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…
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 ru…
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 f…