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Sign-balance of excedances over mod-k-alternating permutations and gamma-positivity
- Publication Year :
- 2024
-
Abstract
- A permutation is called mod-k-alternating if its entries are restricted to having the same remainder as the index, modulo some integer $k \geq 1.$ In this paper, we find the sign-balance for mod-k-alternating permutations with respect to the statistic excedance. Moreover, we study the sign-balance for excedances over mod-k-alternating derangements. The results are obtained by constructing suitable matrices and connecting their determinants with the signed excedance enumeration of mod-k-alternating permutations. As an application of the signed excedance enumeration, we prove that when $n \equiv k \pmod {2k}$, the excedance enumerating polynomials over the even and odd mod-k-alternating permutations, starting with a fixed remainder, are gamma-positive.<br />Comment: Comments are welcome
- Subjects :
- Mathematics - Combinatorics
05A15, 15A15, 05E99
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.21755
- Document Type :
- Working Paper