Efficient Weighted Counting of Multiset Derangements

TL;DR

This paper introduces an efficient method for computing weighted counts of multiset derangements using advanced algorithms, building on classical work from the 1970s to improve computational techniques.

Contribution

The paper combines the Almkvist-Zeilberger algorithm with a weighted Laguerre integral to enhance the calculation of multiset derangement weight enumerators.

Findings

Efficient computation of multiset derangement weight enumerators.

Extension of classical methods with modern algorithmic techniques.

Demonstrates practical improvements over previous approaches.

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.