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arXiv · 2408.00607

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

Noura Alshammari·David Bevan
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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.

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Noura Alshammari, David Bevan. 2024-08-01. On the asymptotic enumeration and limit shapes of monotone grid classes of permutations. https://doi.org/10.46298/dmtcs.14018

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