Both Neou ; Romeo Rizzi ; Stéphane Vialette - Permutation Pattern matching in (213, 231)-avoiding permutations

dmtcs:1329 - Discrete Mathematics & Theoretical Computer Science, March 22, 2017, Vol. 18 no. 2, Permutation Patterns 2015 -
Permutation Pattern matching in (213, 231)-avoiding permutationsArticle

Authors: Both Neou 1; Romeo Rizzi ORCID2; Stéphane Vialette ORCID1

Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two size-3 permutations 213 and 231. For the special case where only σ avoids 213 and 231, we present a O(max(kn 2 , n 2 log log n)-time algorithm. We extend our research to bivincular patterns that avoid 213 and 231 and present a O(kn 4)-time algorithm. Finally we look at the related problem of the longest subsequence which avoids 213 and 231.

Volume: Vol. 18 no. 2, Permutation Patterns 2015
Section: Permutation Patterns
Published on: March 22, 2017
Accepted on: March 22, 2017
Submitted on: March 16, 2017
Keywords: Pattern Avoidance,Pattern Matching,(213 231)-avoiding permutation,Permutation Pattern,Permutation Class,[INFO.INFO-BI] Computer Science [cs]/Bioinformatics [q-bio.QM],[INFO.INFO-CC] Computer Science [cs]/Computational Complexity [cs.CC]

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