Pattern avoidance in non-crossing and non-nesting permutations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908355280240640 |
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| author | Archer, Kassie Laudone, Robert P. |
| author_facet | Archer, Kassie Laudone, Robert P. |
| contents | Non-crossing and non-nesting permutations are variations of the well-known Stirling permutations. A permutation $π$ on $\{1,1,2,2,\ldots, n,n\}$ is called non-crossing if it avoids the crossing patterns $\{1212,2121\}$ and is called non-nesting if it avoids the nesting patterns $\{1221,2112\}.$ Pattern avoidance in these permutations has been considered in recent years, but it has remained open to enumerate the non-crossing and non-nesting permutations that avoid a single pattern of length 3. In this paper, we provide generating functions for those non-crossing and non-nesting permutations that avoid the pattern 231 (and, by symmetry, the patterns 132, 213, or 312). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_13309 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pattern avoidance in non-crossing and non-nesting permutations Archer, Kassie Laudone, Robert P. Combinatorics 05A05, 05A15 Non-crossing and non-nesting permutations are variations of the well-known Stirling permutations. A permutation $π$ on $\{1,1,2,2,\ldots, n,n\}$ is called non-crossing if it avoids the crossing patterns $\{1212,2121\}$ and is called non-nesting if it avoids the nesting patterns $\{1221,2112\}.$ Pattern avoidance in these permutations has been considered in recent years, but it has remained open to enumerate the non-crossing and non-nesting permutations that avoid a single pattern of length 3. In this paper, we provide generating functions for those non-crossing and non-nesting permutations that avoid the pattern 231 (and, by symmetry, the patterns 132, 213, or 312). |
| title | Pattern avoidance in non-crossing and non-nesting permutations |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2502.13309 |