Authors: Both Neou ¹; Romeo Rizzi ²; Stéphane Vialette ¹

• 1 Laboratoire d'Informatique Gaspard-Monge
• 2 Department of Computer Science [Verona]

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.