报告题目：On signed Mahonian polynomials
报告摘要：The distribution of the major index with sign the inversion number over symmetric group is given by Gessel and Simion as
and is generalized to Coxeter groups of type Bn and Dn by Adin-Gessel-Roichman and Biagioli-Caselli, respectively.
In this talk we will show various new signed Mahonian polynomials over Coxeter groups of type Bn and Dn not mentioned in literature, and then extend this concept to the complex reflection group G(r, n) := Cr ≀ Sn. In the latter case the ‘sign’ is taken to be any of the 2r 1-dim characters χa,b and the ‘Mahonian statistic’ is the lmaj defined by Bagno in 2004 and the sorting index sor defined by Petersen in 2011 and then extended by the author in 2015. We also investigate the signed counting on G(r, n) for some statistics with the distribution [r]q [2r]q · · · [nr]q.
报告人简介：罗元勋，厦门大学数学科学学院副教授，研究方向为计数组合、图论、组合设计及其在通讯领域的应用。目前已在Advances in Applied Mathematics、SIAM Discrete Mathematics、Designs Codes and Cryptography、IEEE Internet of Things、IEEE Transaction on Information Theory 等国际期刊发表20余篇论文。