Efficient Weighted Counting of Multiset Derangements
Combinatorics
2025-01-09 v1
Abstract
We use the Almkvist-Zeilberger algorithm, combined with a weighted version of the Even-Gillis Laguerre integral due to Foata and Zeilberger, in order to efficiently compute weight enumerators of multiset derangements according to the number of cycles. The present paper is inspired by important previous work by Mourad Ismail and his collaborators, done in the late 1970s, but still useful after all these years.
Cite
@article{arxiv.2501.04189,
title = {Efficient Weighted Counting of Multiset Derangements},
author = {Shalosh B. Ekhad and Doron Zeilberger},
journal= {arXiv preprint arXiv:2501.04189},
year = {2025}
}
Comments
6 pages. Dedicated to Mourad E.H. Ismail on his 80th birthday