Inversions in Colored Permutations, Derangements, and Involutions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912358577733632 |
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| author | Ahmia, Moussa Ramírez, José L. Villamizar, Diego |
| author_facet | Ahmia, Moussa Ramírez, José L. Villamizar, Diego |
| contents | Arslan, Altoum, and Zaarour introduced an inversion statistic for generalized symmetric groups. In this work, we study the distribution of this statistic over colored permutations, including derangements and involutions. By establishing a bijective correspondence between colored permutations and colored Lehmer codes, we develop a unified framework for enumerating colored Mahonian numbers and analyzing their combinatorial properties. We derive explicit formulas, recurrence relations, and generating functions for the number of inversions in these families, extending classical results to the colored setting. We conclude with explicit expressions for inversions in colored derangements and involutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01550 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inversions in Colored Permutations, Derangements, and Involutions Ahmia, Moussa Ramírez, José L. Villamizar, Diego Combinatorics 05A05, 05A15, 05A19 Arslan, Altoum, and Zaarour introduced an inversion statistic for generalized symmetric groups. In this work, we study the distribution of this statistic over colored permutations, including derangements and involutions. By establishing a bijective correspondence between colored permutations and colored Lehmer codes, we develop a unified framework for enumerating colored Mahonian numbers and analyzing their combinatorial properties. We derive explicit formulas, recurrence relations, and generating functions for the number of inversions in these families, extending classical results to the colored setting. We conclude with explicit expressions for inversions in colored derangements and involutions. |
| title | Inversions in Colored Permutations, Derangements, and Involutions |
| topic | Combinatorics 05A05, 05A15, 05A19 |
| url | https://arxiv.org/abs/2505.01550 |