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 |
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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