Permutations with few inversions are locally uniform

2019/08/20 by David Bevan, Bevan, David · 1 citation
Computer Science · Mathematics · #05A05 #05A16 #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory

paper · doi:10.48550/arxiv.1908.07277

openalex publication_date 2019/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that permutations with few inversions exhibit a local-global dichotomy in the following sense. Suppose \boldsymbolσ is a permutation chosen uniformly at random from the set of all permutations of [n] with exactly m=m(n)≪ n² inversions. If i

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