Sign-twisted generating functions of the odd length for Weyl groups of type D

2023/03/14 by Gu, Haihang, Yu, Houyi
#05A05 #05A15 #05E16 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2303.07658

Abstract

The odd length in Weyl groups is a new statistic analogous to the classical Coxeter length, and features combinatorial and parity conditions. We establish explicit closed product formulas for the sign-twisted generating functions of the odd length for parabolic quotients of Weyl groups of type D. As a consequence, we verify three conjectures of Brenti and Carnevale on evaluating closed forms for these generating functions. We then give an equivalent condition for the sign-twisted generating functions to be expressible as products of cyclotomic polynomials, settling a conjecture of Stembridge.

Related

• Odd length in Weyl groups
• Odd length for even hyperoctahedral groups and signed generating\n functions
• Signed Mahonian polynomials for classical Weyl groups
• Generator Sets for the Alternating Group
• A new statistic on the hyperoctahedral groups