The runsort permuton

Noga Alon, Colin Defant, Noah Kravitz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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}.

Original languageEnglish
Article number102361
JournalAdvances in Applied Mathematics
StatePublished - Aug 2022


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