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- Title
Statistics on Multisets.
- Authors
Mulay, Shashikant; Wagner, Carl
- Abstract
This paper was inspired by Donald Knuth’s celebrated explanation of the remarkable connection between q-binomial coefficients and integer partitions. In the spirit of Knuth’s proof, we offer a new proof of the well-known result that a certain q-analogue of multinomial coefficients furnishes a q-counting of the set of permutations of an associated multiset of positive integers, according to the number of inversions in such arrangements. Our proof uses the fact that such q-multinomial coefficients enumerate certain classes of chains of subspaces of a finite dimensional vector space over a finite field of cardinality q. Additionally, we investigate the function that counts the number of permutations of a multiset having a fixed number of inversions.
- Subjects
FINITE fields; STATISTICS; BINOMIAL coefficients; INTEGERS; PERMUTATIONS; PARTITIONS (Mathematics)
- Publication
Palestine Journal of Mathematics, 2023, Vol 12, Issue 2, p597
- ISSN
2219-5688
- Publication type
Article