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

Both Neou, Romeo Rizzi, Stéphane Vialette
2017 Discrete Mathematics & Theoretical Computer Science  
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
more » ... look at the related problem of the longest subsequence which avoids 213 and 231.
doi:10.46298/dmtcs.1329 fatcat:wo7fipgr4zazbpxebdpinysk3a