On pattern-avoiding permutons
| Autoři | |
|---|---|
| Rok publikování | 2024 |
| Druh | Článek v odborném periodiku |
| Časopis / Zdroj | Random Structures & Algorithms |
| Fakulta / Pracoviště MU | |
| Citace | |
| www | https://doi.org/10.1002/rsa.21208 |
| Doi | http://dx.doi.org/10.1002/rsa.21208 |
| Klíčová slova | pattern-avoidance; permutations; permutons; removal lemma |
| Popis | 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$$ k $$ 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)$$ left(k-1 ight) $$ many, and this bound is sharp. We use this to give a simple proof of the "permutation removal lemma." |
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