Thresholds for patterns in random permutations with a given number of inversions

Bevan, David and Threlfall, Daniel (2024) Thresholds for patterns in random permutations with a given number of inversions. The Electronic Journal of Combinatorics, 31 (4). P4.6. ISSN 1077-8926 (https://doi.org/10.37236/12601)

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Abstract

We explore how the asymptotic structure of a random permutation of n with m inversions evolves, as m increases, establishing thresholds for the appearance and disappearance of any classical, consecutive or vincular pattern. The threshold for the appearance of a classical pattern depends on the greatest number of inversions in any of its sum indecomposable components.

ORCID iDs

Bevan, David ORCID logoORCID: https://orcid.org/0000-0001-7179-2285 and Threlfall, Daniel;
CORE (COnnecting REpositories)