A combinatorial interpretation of Mahonian numbers of type B
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911830199238656 |
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| author | Arslan, Hasan |
| author_facet | Arslan, Hasan |
| contents | In this paper, we first introduce the number of signed permutations with exactly $k$ inversions, which is denoted by $i_B(n,k)$ and called \textit{Mahonian numbers of type $B$}. Then we provide a recurrence relation for the Mahonian numbers $i_B(n,k)$. In addition, we give an explicit recursive description for the summation of inversions of all permutations in the hyperoctahedral group $B_n$, denoted by $\mathcal{B}_n$. Furthermore, we enumerate the total number of inversions in permutations in the hyperoctahedral group $B_n$ concretely with the help of an inversion statistic and a backward permutation concepts on $B_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A combinatorial interpretation of Mahonian numbers of type B Arslan, Hasan Combinatorics 05A05, 05A15, 05A30 In this paper, we first introduce the number of signed permutations with exactly $k$ inversions, which is denoted by $i_B(n,k)$ and called \textit{Mahonian numbers of type $B$}. Then we provide a recurrence relation for the Mahonian numbers $i_B(n,k)$. In addition, we give an explicit recursive description for the summation of inversions of all permutations in the hyperoctahedral group $B_n$, denoted by $\mathcal{B}_n$. Furthermore, we enumerate the total number of inversions in permutations in the hyperoctahedral group $B_n$ concretely with the help of an inversion statistic and a backward permutation concepts on $B_n$. |
| title | A combinatorial interpretation of Mahonian numbers of type B |
| topic | Combinatorics 05A05, 05A15, 05A30 |
| url | https://arxiv.org/abs/2404.05099 |