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Signed Mahonian polynomials for major and sorting indices
- Publication Year :
- 2013
-
Abstract
- We derive some new signed Mahonian polynomials over the complex reflection group $G(r,1,n)=C_r\wr\mathfrak{S}_n$, where the "sign" is taken to be any of the $2r$ $1$-dim characters and the "Mahonian" statistics are the $\mathsf{lmaj}$ defined by Bagno and the $\mathsf{sor}$ defined by Eu et al. Various new signed Mahonian polynomials over Coxeter groups of types $B_n$ and $D_n$ are derived as well. We also investigate the signed counting polynomials on $G(r,1,n)$ for those statistics with the distribution $[r]_q[2r]_q\cdots [nr]_q$.<br />Comment: 22 pages, 1 figure
- Subjects :
- Mathematics - Combinatorics
05A05, 05A19
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1311.5173
- Document Type :
- Working Paper