Over-Mahonian numbers: Basic properties and unimodality
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915043317121024 |
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| author | Kessouri, Ali Ahmia, Moussa Mesbahi, Salim |
| author_facet | Kessouri, Ali Ahmia, Moussa Mesbahi, Salim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10487 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Over-Mahonian numbers: Basic properties and unimodality Kessouri, Ali Ahmia, Moussa Mesbahi, Salim Combinatorics 05A05, 05A15, 05A30, 11B73 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. |
| title | Over-Mahonian numbers: Basic properties and unimodality |
| topic | Combinatorics 05A05, 05A15, 05A30, 11B73 |
| url | https://arxiv.org/abs/2406.10487 |