Sums of Schubert structure constants with bounded Coxeter length

Abstract

Pak–Robichaux recently introduced a signed puzzle rule for Schubert structure constants, which they use to show that sums γ k ( n ) of these constants with a bounded number of inversions are polynomial. We give a different, conceptual proof that γ k ( n ) is (eventually) polynomial, which computes its lead term and extends to all classical Lie types.