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

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Alshammari, Noura and Bevan, David (2025) On the asymptotic enumeration and limit shapes of monotone grid classes of permutations. Discrete Mathematics and Theoretical Computer Science, 27 (1). 2. ISSN 1365-8050 (https://doi.org/10.46298/dmtcs.14018)

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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.

ORCID iDs

Alshammari, Noura and Bevan, David ORCID logoORCID: https://orcid.org/0000-0001-7179-2285;
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