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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.03155 |
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| _version_ | 1866913642938630144 |
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| author | Birmajer, Daniel Gil, Juan B. Tirrell, Jordan O. Weiner, Michael D. |
| author_facet | Birmajer, Daniel Gil, Juan B. Tirrell, Jordan O. Weiner, Michael D. |
| contents | In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF permutations for classical and pairs of patterns of size 3. In particular, for the patterns 123 and 231, we rely on combinatorial arguments and the fixed-point distribution of general permutations avoiding these patterns. We briefly discuss 123-avoiding permutations with two fixed points and offer a conjecture for their enumeration by the distance between their fixed points. For the pattern 231, we also give a direct argument that uses a bijection to ordered forests. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03155 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pattern-avoiding stabilized-interval-free permutations Birmajer, Daniel Gil, Juan B. Tirrell, Jordan O. Weiner, Michael D. Combinatorics 05A05, 05A15 In this paper, we study pattern avoidance for stabilized-interval-free (SIF) permutations. These permutations are contained in the set of indecomposable permutations and in the set of derangements. We enumerate pattern-avoiding SIF permutations for classical and pairs of patterns of size 3. In particular, for the patterns 123 and 231, we rely on combinatorial arguments and the fixed-point distribution of general permutations avoiding these patterns. We briefly discuss 123-avoiding permutations with two fixed points and offer a conjecture for their enumeration by the distance between their fixed points. For the pattern 231, we also give a direct argument that uses a bijection to ordered forests. |
| title | Pattern-avoiding stabilized-interval-free permutations |
| topic | Combinatorics 05A05, 05A15 |
| url | https://arxiv.org/abs/2306.03155 |