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Pré-Publication, Document De Travail Année : 2015

Pattern matching in (213, 231)-avoiding permutations

Résumé

Given permutations $\sigma \in S_k$ and $\pi \in S_n$ with $k < n$, the pattern matching problem is to decide whether $\pi$ matches $\sigma$ as an order-isomorphic subsequence. We give a linear-time algorithm in case both $\pi$ and $\sigma$ avoid the two size-$3$ permutations $213$ and $231$. For the special case where only $\sigma$ 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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Both Emerite Neou, Roméo Rizzi, Stéphane Vialette. Pattern matching in (213, 231)-avoiding permutations. 2015. ⟨hal-01219299v1⟩
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