Mahonian-Stirling statistics for partial permutations
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911823557558272 |
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| author | Ding, Ming-Jian Zeng, Jiang |
| author_facet | Ding, Ming-Jian Zeng, Jiang |
| contents | Recently Cheng et al. (Adv. in Appl. Math. 143 (2023) 102451) generalized the inversion number to partial permutations, which are also known as Laguerre digraphs, and asked for a suitable analogue of MacMahon's major index. We provide such a major index, namely, the corresponding maj and inv statistics are equidistributed, and exhibit a Haglund-Remmel-Wilson type identity. We then interpret some Jacobi-Rogers polynomials in terms of Laguerre digraphs generalizing Deb and Sokal's alternating Laguerre digraph interpretation of some special Jacobi-Rogers polynomials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_01465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mahonian-Stirling statistics for partial permutations Ding, Ming-Jian Zeng, Jiang Combinatorics Recently Cheng et al. (Adv. in Appl. Math. 143 (2023) 102451) generalized the inversion number to partial permutations, which are also known as Laguerre digraphs, and asked for a suitable analogue of MacMahon's major index. We provide such a major index, namely, the corresponding maj and inv statistics are equidistributed, and exhibit a Haglund-Remmel-Wilson type identity. We then interpret some Jacobi-Rogers polynomials in terms of Laguerre digraphs generalizing Deb and Sokal's alternating Laguerre digraph interpretation of some special Jacobi-Rogers polynomials. |
| title | Mahonian-Stirling statistics for partial permutations |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2404.01465 |