Pattern Matching for Separable Permutations

Given a permutation \(\pi \) (called the text) of size n and another permutation \(\sigma \) (called the pattern) of size k, the NP-complete permutation pattern matching problem asks whether \(\sigma \) occurs in \(\pi \) as an order-isomorphic subsequence. In this paper, we focus on separable permutations (those permutations that avoid both 2413 and 3142, or, equivalently, that admit a separating tree). The main contributions presented in this paper are as follows.

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