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arXiv · 2406.10487

Over-Mahonian numbers: Basic properties and unimodality

Ali Kessouri·Moussa Ahmia·Salim Mesbahi
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Abstract

In this paper, we introduce the concept of the over-Mahonian number, which counts the overlined permutations of length $n$ with $k$ inversions, allowing the first elements associated with the inversions to be independently overlined or not. We explore its properties and combinatorial interpretations through lattice paths, overpartitions, and tilings, and provide a combinatorial proof demonstrating that these numbers form a log-concave and unimodal sequence.

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Ali Kessouri, Moussa Ahmia, Salim Mesbahi. 2024-12-02. Over-Mahonian numbers: Basic properties and unimodality. https://arxiv.org/abs/2406.10487

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