2024/06/15 by Ali Kessouri, Kessouri, Ali, Moussa Ahmia +3
Arts and Humanities · Social Sciences · #05A05 #05A15 #05A30 #11B73 #Combinatorics (math.CO) #FOS: Mathematics #Linguistic Variation and Morphology #Names, Identity, and Discrimination Research #Syntax, Semantics, Linguistic Variation
paper · pdf · doi:10.48550/arxiv.2406.10487
openalex publication_date 2024/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.