Affine Deodhar Diagrams and Rational Dyck Paths

Abstract: Given a bounded affine permutation $f$, we introduce affine Deodhar diagrams for $f$, similar to affine pipe dreams introduced by Snider. We explore combinatorial moves between these diagrams and, as an application, use these moves to establish a bijection between Deodhar diagrams and rational Dyck paths for a special class of bounded affine permutations. This resolves an open problem posed by Galashin and Lam.

combinatorics

Audience: learners

UCLA Combinatorics Forum

Series comments: This quarter, the talks will be in-person with no Zoom livestream.