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On r-Euler-Mahonian statistics for multipermutations
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DOI：10.1016/j.jcta.2026.106165.png)
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Abstract
En 中文
A pair (st(1), st(2)) of permutation statistics is said to be r-Euler-Mahonian over multipermutations if (st(1), st(2)) and (rdes, rmaj) are equidistributed over the set G(M) of all multipermutations of M for any given multiset M, where rdes denotes therdescent number and rmaj denotes thermajor index introduced by Rawlings. In this paper, we shall introduce thergap excedance number rexc and thergap Denert's statistic rden for multipermutations and prove that (rexc, rden) is r-Euler-Mahonian over multipermutations, thereby extending Liu's result on permutations to multipermutations. When r = 1, our result recovers the equidistribution of (des, maj) and (exc, den) over G(M) derived by Han. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords:
r-major index
r-descent number
r-gap Denert's statistic
r-gap excedance number
r-Euler-Mahonian statistic
Journal
J
IF:
1.2
Papers:
42
Citations:
0