Permutations with only reduced co-BPDs

TL;DR

This paper characterizes permutations whose bumpless pipe dreams have only reduced co-BPDs using pattern avoidance, advancing understanding of combinatorial structures related to Schubert and Grothendieck polynomials.

Contribution

It provides a pattern-avoidance characterization for permutations with only reduced co-BPDs, addressing a problem posed by Weigandt.

Findings

Identifies seven specific patterns characterizing these permutations

Establishes a combinatorial criterion for reduced co-BPDs

Enhances understanding of BPDs in algebraic combinatorics

Abstract

Bumpless pipe dreams (BPDs) are combinatorial objects used in the study of Schubert and Grothendieck polynomials. Weigandt recently introduced a co-BPD object associated to each BPD and used them to give an analogue to the change of bases formulas of Lenart and Lascoux between these polynomials. She posed the problem of characterizing the set of permutations whose BPDs have only reduced co-BPDs. We give a pattern-avoidance characterization for these permutations using a set of seven patterns.