Geodesic
Permutation Pattern matching in (213, 231)-avoiding permutations
Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2.

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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. 
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     author = {Neou, Both and Rizzi, Romeo and Vialette, St\'ephane},
     title = {Permutation {Pattern} matching in (213, 231)-avoiding permutations},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2015-2016},
     doi = {10.46298/dmtcs.1329},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1329/}
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Neou, Both; Rizzi, Romeo; Vialette, Stéphane. Permutation Pattern matching in (213, 231)-avoiding permutations. Discrete mathematics & theoretical computer science, Permutation Patterns 2015, Tome 18 (2015-2016) no. 2. doi : 10.46298/dmtcs.1329. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.1329/

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