Limit theorems for fixed point biased permutations avoiding a pattern of length three
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915850623123456 |
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| author | Chelikavada, Aksheytha Panzo, Hugo |
| author_facet | Chelikavada, Aksheytha Panzo, Hugo |
| contents | We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution towards favoring permutations with more or fewer fixed points than is typical under the uniform distribution. One case we study features a phase transition where the limiting distribution changes abruptly from negative binomial to Rayleigh to normal depending on the bias parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_04623 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Limit theorems for fixed point biased permutations avoiding a pattern of length three Chelikavada, Aksheytha Panzo, Hugo Probability Combinatorics 05A05, 60C05, 60F05 (Primary) 05A15, 68Q87 (Secondary) We prove limit theorems for the number of fixed points occurring in a random pattern-avoiding permutation distributed according to a one-parameter family of biased distributions. The bias parameter exponentially tilts the distribution towards favoring permutations with more or fewer fixed points than is typical under the uniform distribution. One case we study features a phase transition where the limiting distribution changes abruptly from negative binomial to Rayleigh to normal depending on the bias parameter. |
| title | Limit theorems for fixed point biased permutations avoiding a pattern of length three |
| topic | Probability Combinatorics 05A05, 60C05, 60F05 (Primary) 05A15, 68Q87 (Secondary) |
| url | https://arxiv.org/abs/2311.04623 |