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 language | English |
|---|---|
| Pages (from-to) | 189-221 |
| Number of pages | 33 |
| Journal | Israel Journal of Mathematics |
| Volume | 151 |
| DOIs | |
| State | Published - 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
Funding
* 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
| Funders | Funder number |
|---|---|
| European Commission | HPRN-CT-2001-00272 |