On pattern-avoiding permutons

Random Structures and Algorithms Pub Date : 2024-01-29 DOI:10.1002/rsa.21208

Frederik Garbe, Jan Hladký, Gábor Kun, Kristýna Pekárková

引用次数: 0

Abstract

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) $$ \left(k-1\right) $$

many, and this bound is sharp. We use this to give a simple proof of the “permutation removal lemma.”

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关于规避模式的 permutons

排列极限理论引出了称为 permutons 的极限对象，它们是单位平方上的某些博尔量。我们证明，避开阶数 k$$ k $$ 的给定置换的置换子具有特别简单的结构。也就是说，几乎每条分解 permuton 的纤维（比如说，沿着 x 轴）都只由原子组成，最多只有 (k-1)$$ \left(k-1\right) $$ 个，而且这个约束是尖锐的。我们利用这一点给出了 "包络去除稃证 "的简单证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Structures and Algorithms

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