Eulerian Polynomials for Bidirected Graphs
Panya Sukphrane
Department of Mathematics
Faculty Supervisor: Matthias Beck
The descent and inversion statistics are two statistics of interest from combinatorics that are defined for the permutation group S_n. MacMahon introduced the major index statistic which has the same generating function as the inversion statistic. Foata and Zeilberger (1995) defined the inversion and descent polynomials for digraphs and observed that the classical descent and inversion polynomials could be viewed as special cases of Ddescents on certain graphs. Celano et al (2023) investigated the evaluations of the Ddescents at -1. We extend these results to signed permutations on bidirected graphs, with special cases giving Euler-Mahonian statistics for the hyperoctahedral group.