University of Minnesota Combinatorics Seminar: 2021-2022

Date: 09/24/2021

Speaker: Daoji Huang

Bijective Combinatorics in Schubert Calculus with Pipe Dreams and Bumpless Pipe Dreams
Pipe dreams and bumpless pipe dreams both give combinatorial formulas for Schubert polynomials. As a result, many important identities in Schubert calculus can be understood through pipe dreams and/or bumpless pipe dreams. Since the discovery of bumpless pipe dreams, a direct weight-preserving bijection between pipe dreams and bumpless pipe dreams has been of great interest. In this talk, we present such a bijection, and establish its canonical nature by showing that it preserves Monk's rule. We also remark that the technical recipe used in this bijection has been useful in a few other contexts, including a combinatorial rule for Schubert structure constants in the separated descent Schubert problem. The work on the canonical bijection is joint with Yibo Gao.

Bijective Combinatorics in Schubert Calculus with Pipe Dreams and Bumpless Pipe Dreams

Pipe dreams and bumpless pipe dreams both give combinatorial formulas for Schubert polynomials. As a result, many important identities in Schubert calculus can be understood through pipe dreams and/or bumpless pipe dreams. Since the discovery of bumpless pipe dreams, a direct weight-preserving bijection between pipe dreams and bumpless pipe dreams has been of great interest. In this talk, we present such a bijection, and establish its canonical nature by showing that it preserves Monk's rule. We also remark that the technical recipe used in this bijection has been useful in a few other contexts, including a combinatorial rule for Schubert structure constants in the separated descent Schubert problem. The work on the canonical bijection is joint with Yibo Gao.