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Conference Papers Year : 2019

Unshuffling Permutations

Abstract

Given permutations π, σ1 and σ2 , the permutation π (viewed as a string) is said to be a shuffle of σ1 and σ2 , in symbols π ∈ σ1 σ2 , if π can be formed by interleaving the letters of two strings p1 and p2 that are order-isomorphic to σ1 and σ2 , respectively. Given a permutation π ∈ S2n and a bijective mapping f : Sn → Sn , the f -Unshuffle-Permutation problem is to decide whether there exists a permutation σ ∈ Sn such that π ∈ σ f (σ). We consider here this problem for the following bijective mappings: inversion, reverse, complementation, and all their possible compositions. In particular, we present combinatorial results about the permutations accepted by this problem. As main results, we obtain that this problem is NP-complete when f is the reverse, the complementation, or the composition of the reverse with the complementation.
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Dates and versions

hal-02304028 , version 1 (14-02-2023)

Identifiers

Cite

Guillaume Fertin, Samuele Giraudo, Sylvie Hamel, Stéphane Vialette. Unshuffling Permutations: Trivial Bijections and Compositions. TAMC, Apr 2019, Kitakyushu, Japan. pp.242-261, ⟨10.1007/978-3-030-14812-6_15⟩. ⟨hal-02304028⟩
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