arXiv subjects
Publications and source records attributed to Ningxin Zhang.
We obtain a novel formula for characteristic polynomials of deformations of the Braid arrangement using the notion of levels of regions. As an application, we recover and strengthen results of Chen et al. on the characteristic polynomial of several specific types of hyperplane arrangements via much simpler arguments. Our theorem also generalizes to type B.
Let $v(n)$ be the largest principal specialization of Schubert polynomials for layered permutations $v(n) := \max_{w \in \mathcal{L}_n} \mathfrak{S}_w(1,\ldots,1)$. Morales, Pak and Panova proved that there is a limit \[\lim_{n \to \infty} \frac{\log v(n)}{n^2},\] 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 $\mathfrak{S}_w(1,q,q^2,\ldots)$ for multi-layered permutations when $q$ equals a root of unity.