Abstract
We count derangements, involutions and unimodal elements in the wreath product Cr ≀ Sn by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric group Sn and on the hyperoctahedral group Bn when r = 1, 2, respectively. Copyright © 2010 The Hebrew University Magnes Press.
| Original language | English |
|---|---|
| Pages (from-to) | 425-448 |
| Journal | Israel Journal of Mathematics |
| Volume | 179 |
| Issue number | 1 |
| Early online date | 31 Oct 2010 |
| DOIs | |
| Publication status | Published - Dec 2010 |
Citation
Chow, C. O., & Mansour, T. (2010). Counting derangements, involutions and unimodal elements in the wreath product Cr ≀ Sn. Israel Journal of Mathematics, 179(1), 425-448. doi: 10.1007/s11856-010-0088-8Keywords
- Recurrence relation
- Symmetric group
- Toric variety
- Coxeter group
- Wreath product