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Pré-Publication, Document De Travail Année : 2016

Pattern matching in (213, 231)-avoiding permutations

Résumé

Given permutations σ ∈ S k and π ∈ Sn with k < n, the pattern matching problem is to decide whether σ occurs 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.
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Dates et versions

hal-01219299 , version 1 (28-10-2015)
hal-01219299 , version 2 (03-03-2016)
hal-01219299 , version 3 (14-10-2016)
hal-01219299 , version 4 (02-02-2017)
hal-01219299 , version 5 (02-03-2017)
hal-01219299 , version 6 (12-03-2017)

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Neou Both Emerite, Romeo Rizzi, Stéphane Vialette. Pattern matching in (213, 231)-avoiding permutations. 2016. ⟨hal-01219299v2⟩
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