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Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2017

Permutation Pattern matching in (213, 231)-avoiding permutations

Résumé

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(kn², n² 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)

Licence

Domaine public

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Both Emerite Neou, Romeo Rizzi, Stéphane Vialette. Permutation Pattern matching in (213, 231)-avoiding permutations. Discrete Mathematics and Theoretical Computer Science, 2017, Vol. 18 no. 2, Permutation Patterns 2015 (2), pp.#14.1-22. ⟨10.46298/dmtcs.1329⟩. ⟨hal-01219299v6⟩
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