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An Equipartition Property for the Distribution of Multiset Permutation Inversions

✍ Scribed by S. Brunetti; A. Del Lungo; F. Del Ristoro

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 91 KB
Volume: 27
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.2001.0725

No coin nor oath required. For personal study only.

✦ Synopsis

The purpose of this paper is to present some enumerative results concerning the class k of permutations of the multiset 1 m 1 2 m 2 r m r having inversion number congruent to k modulo n, with n = m 1 + m 2 + • • • + m r and 0 ≤ k < n. We show that the enumeration of this family of permutations is connected to gcd m 1 m 2 m r , and if gcd

for each 0 ≤ k < n. Finally, some applications of these properties concerning the q-multinomial coefficient are found.

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