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Over-Mahonian numbers: Basic properties and unimodality
Preprint
14 June 2024
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Abstract
In this paper, we propose the number of permutations of length \(n\) having \(k\) overlined inversions, which we call over-Mahonian number. We study useful properties and some combinatorial interpretations by lattice paths/overpartitions and tilings. Furthermore, we prove combinatorially that these numbers form a log-concave sequence and therefore unimodal.