On the asymptotic enumeration and limit shapes of monotone grid classes of permutations

2024/08/01 by Noura Alshammari, Alshammari, Noura, David Bevan +1
Computer Science · Mathematics · #05A05 #05A16 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2408.00607

openalex publication_date 2024/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the gridded permutations, finding the asymptotic distribution of points between the cells in a typical large gridded permutation, and analysing in detail the ways in which a typical permutation can be gridded. We also determine the limit shape of any connected monotone grid class.

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