Frederik Garbe, Jan Hladký, Gábor Kun, Kristýna Pekárková
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引用次数: 0
摘要
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。
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 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 many, and this bound is sharp. We use this to give a simple proof of the “permutation removal lemma.”
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