On pattern-avoiding permutons
| Authors | |
|---|---|
| Year of publication | 2024 |
| Type | Article in Periodical |
| Magazine / Source | Random Structures & Algorithms |
| MU Faculty or unit | |
| Citation | |
| web | https://doi.org/10.1002/rsa.21208 |
| Doi | http://dx.doi.org/10.1002/rsa.21208 |
| Keywords | pattern-avoidance; permutations; permutons; removal lemma |
| Description | 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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