Limit theorems for fixed point biased permutations avoiding a pattern of length three.
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| Title: | Limit theorems for fixed point biased permutations avoiding a pattern of length three. |
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| Authors: | Chelikavada, Aksheytha1, Panzo, Hugo2 |
| Source: | Discrete Mathematics & Theoretical Computer Science (DMTCS). 2026, Vol. 28 Issue 2, p1-17. 17p. |
| Subjects: | Permutations, Limit theorems, Distribution (Probability theory), Phase transitions, Rayleigh model, Gaussian distribution, Negative binomial distribution |
| Abstract: | 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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