On pattern-avoiding permutons
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866929589952970752 |
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| author | Garbe, Frederik Hladký, Jan Kun, Gábor Pekárková, Kristýna |
| author_facet | Garbe, Frederik Hladký, Jan Kun, Gábor Pekárková, Kristýna |
| contents | The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order $k$ have a particularly simple structure. Namely, almost every fiber of the disintegration of the permuton (say, along the x-axis) consists only of atoms, at most $(k-1)$ many, and this bound is sharp. We use this to give a simple proof of the `permutation removal lemma'. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12712 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On pattern-avoiding permutons Garbe, Frederik Hladký, Jan Kun, Gábor Pekárková, Kristýna Combinatorics 05A05 G.2.1 The theory of limits of permutations leads to limit objects called permutons, which are certain Borel measures on the unit square. We prove that permutons avoiding a given permutation of order $k$ have a particularly simple structure. Namely, almost every fiber of the disintegration of the permuton (say, along the x-axis) consists only of atoms, at most $(k-1)$ many, and this bound is sharp. We use this to give a simple proof of the `permutation removal lemma'. |
| title | On pattern-avoiding permutons |
| topic | Combinatorics 05A05 G.2.1 |
| url | https://arxiv.org/abs/2208.12712 |