Roots of descent polynomials and an algebraic inequality on hook lengths

Abstract

We prove a conjecture by Diaz-Lopez et al. that bounds the roots of descent polynomials. To do so, we prove an algebraic inequality, which we refer to as the "Slice and Push Inequality." This inequality compares expressions that come from Naruse's hook-length formula for the number of standard Young tableaux of a skew shape.

arXiv comment24 pages, 8 figures. Comments are very welcome!