A relation on 132-avoiding permutation patterns

Abstract : A permutation $σ$ contains the permutation $τ$ if there is a subsequence of $σ$ order isomorphic to $τ$. A permutation $σ$ is $τ$-avoiding if it does not contain the permutation $τ$. For any $n$, the popularity of a permutation $τ$, denoted $A$$n$($τ$), is the number of copies of $τ$ contained in the set of all 132-avoiding permutations of length $n$. Rudolph conjectures that for permutations $τ$ and $μ$ of the same length, $A$$n$($τ$) ≤ $A$$n$($μ$) for all $n$ if and only if the spine structure of $τ$ is less than or equal to the spine structure of $μ$ in refinement order. We prove one direction of this conjecture, by showing that if the spine structure of $τ$ is less than or equal to the spine structure of $μ$, then $A$$n$($τ$) ≤ $A$$n$($μ$) for all $n$. We disprove the opposite direction by giving a counterexample, and hence disprove the conjecture.
Type de document :
Article dans une revue
Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.285-302
Liste complète des métadonnées

Littérature citée [6 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-01349056
Contributeur : Coordination Episciences Iam <>
Soumis le : mardi 26 juillet 2016 - 17:57:33
Dernière modification le : jeudi 7 septembre 2017 - 01:03:44

Fichier

2375-9839-1-PB.pdf
Accord explicite pour ce dépôt

Identifiants

  • HAL Id : hal-01349056, version 1

Collections

Citation

Natalie Aisbett. A relation on 132-avoiding permutation patterns. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2015, Vol. 17 no.2 (2), pp.285-302. 〈hal-01349056〉

Partager

Métriques

Consultations de la notice

34

Téléchargements de fichiers

166