Asymptotics of self-overlapping permutations - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Asymptotics of self-overlapping permutations

Résumé

In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a permutation can be represented as a sequence of non-self-overlapping ones. The above structural decomposition allows us to obtain equations for the corresponding generating functions, as well as the complete asymptotic expansions for the probability that a large random permutation is (non-)self-overlapping. In particular, we show that almost all permutations are non-self-overlapping, and that the corresponding asymptotic expansion has the self-reference property: the involved coefficients count non-self-overlapping permutations once again. We also establish complete asymptotic expansions of the distributions of very tight non-self-overlapping patterns, and discuss the similarities of the non-self-overlapping permutations to other permutation building blocks, such as indecomposable and simple permutations, as well as their associated asymptotics.
Fichier principal
Vignette du fichier
self-overlapping-permutations.pdf (264.57 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04297210 , version 1 (21-11-2023)
hal-04297210 , version 2 (27-06-2024)

Identifiants

Citer

Khaydar Nurligareev, Sergey Kirgizov. Asymptotics of self-overlapping permutations. 2023. ⟨hal-04297210v2⟩
7 Consultations
13 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More