TY - JOUR

T1 - The runsort permuton

AU - Alon, Noga

AU - Defant, Colin

AU - Kravitz, Noah

N1 - Publisher Copyright:
© 2022 Elsevier Inc.

PY - 2022/8

Y1 - 2022/8

N2 - Suppose we choose a permutation π uniformly at random from Sn. Let runsort(π) be the permutation obtained by sorting the ascending runs of π into lexicographic order. Alexandersson and Nabawanda recently asked if the plot of runsort(π), when scaled to the unit square [0,1]2, converges to a limit shape as n→∞. We answer their question by showing that the measures corresponding to the scaled plots of these permutations runsort(π) converge with probability 1 to a permuton (limiting probability distribution) that we describe explicitly. In particular, the support of this permuton is {(x,y)∈[0,1]2:x≤ye1−y}.

AB - Suppose we choose a permutation π uniformly at random from Sn. Let runsort(π) be the permutation obtained by sorting the ascending runs of π into lexicographic order. Alexandersson and Nabawanda recently asked if the plot of runsort(π), when scaled to the unit square [0,1]2, converges to a limit shape as n→∞. We answer their question by showing that the measures corresponding to the scaled plots of these permutations runsort(π) converge with probability 1 to a permuton (limiting probability distribution) that we describe explicitly. In particular, the support of this permuton is {(x,y)∈[0,1]2:x≤ye1−y}.

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U2 - 10.1016/j.aam.2022.102361

DO - 10.1016/j.aam.2022.102361

M3 - Article

AN - SCOPUS:85129727724

SN - 0196-8858

VL - 139

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102361

ER -