Statistics on wreath products and generalized binomial-stirling numbers

Amitai Regev, Yuval Roichman

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 a MacMahon-type equi-distribution theorem over subsets with prescribed statistics.

Original languageEnglish
Pages (from-to)189-221
Number of pages33
JournalIsrael Journal of Mathematics
Volume151
DOIs
StatePublished - 2006

Bibliographical note

Funding Information:
* Partially supported by Minerva Grant No. 8441 and by EC's IHRP Programme, within the Research Training Network "Algebraic Combinatorics in Europe", grant HPRN-CT-2001-00272. ** Partially supported by EC's IHRP Programme, within the Research Training Network "Algebraic Combinatorics in Europe", grant HPRN-CT-2001-00272. Received April 22, 2004

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