On pattern-avoiding permutons - Garbe, Frederik; Hladký, Jan; Kun, Gábor; Pekárková, Kristýna (Random structures & algorithms, 2024)
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)\ łeft(k-1\right) \ many, and this bound is sharp. We use this to give a simple proof of the “permutation removal lemma.”
Gesehen am 21.11.2024