Principal specializations of Schubert polynomials, multi-layered permutations and asymptotics

Abstract

Let v(n) be the largest principal specialization of Schubert polynomials for layered permutations v(n):=maxw∈Ln⁡Sw(1,…,1). Morales, Pak and Panova proved that there is a limitlimn→∞⁡log⁡v(n)n2, and gave a precise description of layered permutations reaching the maximum. In this paper, we extend Morales Pak and Panova's results to generalized principal specialization Sw(1,q,q2,…) for multi-layered permutations when q equals a root of unity.