A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914629511282688 |
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| author | Park, Jungeun Rizzolo, Douglas |
| author_facet | Park, Jungeun Rizzolo, Douglas |
| contents | We use local limits of Galton-Watson trees to establish local limit theorems for permutations conditioned to avoid a pattern of length three. In the case of 321-avoiding permutations our results resolve an open problem of Pinsky. In the other cases our results give new descriptions of the limiting objects in terms of size-biased Galton-Watson trees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01957 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three Park, Jungeun Rizzolo, Douglas Probability Combinatorics 60C05, 60F05, 60J80 We use local limits of Galton-Watson trees to establish local limit theorems for permutations conditioned to avoid a pattern of length three. In the case of 321-avoiding permutations our results resolve an open problem of Pinsky. In the other cases our results give new descriptions of the limiting objects in terms of size-biased Galton-Watson trees. |
| title | A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three |
| topic | Probability Combinatorics 60C05, 60F05, 60J80 |
| url | https://arxiv.org/abs/2401.01957 |