Thesis

On the asymptotic enumeration of monotone grid classes of permutations

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Awarding institution
  • University of Strathclyde
Date of award
  • 2025
Thesis identifier
  • T17365
Person Identifier (Local)
  • 202156614
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • We find 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 L-shaped, T-shaped, and X-shaped class. We start by looking at the simplest case of the skinny classes with a single row or column. Finding the exact enumeration of grid classes is hard, so our goal is to find the asymptotic enumeration. Our strategy consists of enumerating the gridded permutations, finding the asymptotic distribution of points between the cells in a typical large gridded permutation, and determining in detail the ways in which a typical large M-gridded permutation must be structured so that its underlying permutation σ has exactly ℓ distinct M-griddings. We then combine the previous steps to calculate for each ℓ ≥ 1, the asymptotic probability that σ has exactly ℓ distinct M-griddings. Then we deduce the asymptotic enumeration of the number of permutations in the class.
Advisor / supervisor
  • Bevan, David
Resource Type
DOI

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file details PDF of Thesis T17365 2025-07-17 Público Baixar