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

Let v ( n ) be the largest principal specialization of Schubert polynomials for layered permutations v ( n ) := max w is an element of L n S w (1 , ..., 1). Morales, Pak and Panova proved that there is a limit lim n ->infinity 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 S w (1 , q, q2, ...) for multi-layered permutations when q equals a root of unity. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.