Statistics on Wreath Products and Generalized Binomial-Stirling Numbers
Combinatorics
2007-05-23 v1
Abstract
Various statistics on wreath products are defined via canonical words, "colored" right to left minima and "colored" descents. It is shown that refined counts with respect to these statistics have nice recurrence formulas of binomial-Stirling type. These extended Stirling numbers determine (via matrix inversion) dual systems, which are also shown to have combinatorial realizations within the wreath product. The above setting also gives rise to MacMahon type equi-distribution theorem over subsets with prescribed statistics.
Cite
@article{arxiv.math/0404354,
title = {Statistics on Wreath Products and Generalized Binomial-Stirling Numbers},
author = {Amitai Regev and Yuval Roichman},
journal= {arXiv preprint arXiv:math/0404354},
year = {2007}
}
Comments
36 pages