Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912924523560960 |
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| author | Lv, Shuzhen Zhang, Philip B. |
| author_facet | Lv, Shuzhen Zhang, Philip B. |
| contents | In this paper, we extend recent results by Lv and Kitaev by proving 20 (out of 22 possible) joint equidistributions of mesh patterns 123 and 321 with symmetric shadings, as well as all 36 joint equidistributions of these patterns with minus-antipodal shadings. Our results link several joint equidistributions of mesh patterns to various integer sequences, including unsigned Stirling numbers of the first kind, harmonic numbers, and the numbers of inversion sequences avoiding a certain vincular pattern studied by Lin and Yan. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00357 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings Lv, Shuzhen Zhang, Philip B. Combinatorics 05A05, 05A15 In this paper, we extend recent results by Lv and Kitaev by proving 20 (out of 22 possible) joint equidistributions of mesh patterns 123 and 321 with symmetric shadings, as well as all 36 joint equidistributions of these patterns with minus-antipodal shadings. Our results link several joint equidistributions of mesh patterns to various integer sequences, including unsigned Stirling numbers of the first kind, harmonic numbers, and the numbers of inversion sequences avoiding a certain vincular pattern studied by Lin and Yan. |
| title | Joint equidistributions of mesh patterns 123 and 321 with symmetric and minus-antipodal shadings |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2501.00357 |