Limit Theorems for Fixed Point Biased Pattern Avoiding Involutions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908741647990784 |
|---|---|
| author | Park, Jungeun Rizzolo, Douglas |
| author_facet | Park, Jungeun Rizzolo, Douglas |
| contents | We study fixed point biased involutions that avoid a pattern. For every pattern of length three we obtain limit theorems for the asymptotic distribution of the (appropriately centered and scaled) number of fixed points of a random fixed point biased involution avoiding that pattern. When the pattern being avoided is either $321$, $132$, or $213$, we find a phase transition depending on the strength of the bias. We also obtain a limit theorem for distribution of fixed points when the pattern is $123\cdots k(k+1)$ for any $k$ and partial results when the pattern is $(k+1)k\cdots 321$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_25006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Limit Theorems for Fixed Point Biased Pattern Avoiding Involutions Park, Jungeun Rizzolo, Douglas Probability Combinatorics 60C05, 60F05, 05A05 We study fixed point biased involutions that avoid a pattern. For every pattern of length three we obtain limit theorems for the asymptotic distribution of the (appropriately centered and scaled) number of fixed points of a random fixed point biased involution avoiding that pattern. When the pattern being avoided is either $321$, $132$, or $213$, we find a phase transition depending on the strength of the bias. We also obtain a limit theorem for distribution of fixed points when the pattern is $123\cdots k(k+1)$ for any $k$ and partial results when the pattern is $(k+1)k\cdots 321$. |
| title | Limit Theorems for Fixed Point Biased Pattern Avoiding Involutions |
| topic | Probability Combinatorics 60C05, 60F05, 05A05 |
| url | https://arxiv.org/abs/2512.25006 |