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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.19541 |
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| _version_ | 1866912923622834176 |
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| author | Hohmeier, Kaitlyn Slivken, Erik |
| author_facet | Hohmeier, Kaitlyn Slivken, Erik |
| contents | Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits for permutations sampled uniformly from certain pattern-avoiding classes that are in bijection with the class of permutations avoiding the increasing pattern of length $d+1$. In particular, we will look at a family of permutations whose permuton limit collapses to the unique permuton supported on the line $x + y = 1$ in the unit square, informally known as the anti-diagonal. We prove some general properties about permutons to aid our efforts, which may be useful for proving permuton limits that converge to the anti-diagonal for a broader range of permutation classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Permuton limits for some permutations avoiding a single pattern Hohmeier, Kaitlyn Slivken, Erik Probability Combinatorics Permutons are probability measures on the unit square with uniform marginals that provide a natural way to describe limits of permutations. We are interested in the permuton limits for permutations sampled uniformly from certain pattern-avoiding classes that are in bijection with the class of permutations avoiding the increasing pattern of length $d+1$. In particular, we will look at a family of permutations whose permuton limit collapses to the unique permuton supported on the line $x + y = 1$ in the unit square, informally known as the anti-diagonal. We prove some general properties about permutons to aid our efforts, which may be useful for proving permuton limits that converge to the anti-diagonal for a broader range of permutation classes. |
| title | Permuton limits for some permutations avoiding a single pattern |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2502.19541 |