Algorithmic and algebraic aspects of unshuffling permutations

Abstract : A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the problem of recognizing square permutations from both the point of view of algebra and algorithms. On the one hand, we present some algebraic and combinatorial properties of the shuffle product of permutations. We follow an unusual line consisting in defining the shuffle of permutations by means of an unshuffling operator, known as a coproduct. This strategy allows to obtain easy proofs for algebraic and combinatorial properties of our shuffle product. We besides exhibit a bijection between square (213, 231)-avoiding permutations and square binary words. On the other hand, by using a pattern avoidance criterion on directed perfect matchings, we prove that recognizing square permutations is NP-complete.
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download

https://hal-upec-upem.archives-ouvertes.fr/hal-01797134
Contributor : Samuele Giraudo <>
Submitted on : Wednesday, May 23, 2018 - 3:40:40 PM
Last modification on : Friday, April 12, 2019 - 10:18:10 AM
Long-term archiving on : Friday, August 24, 2018 - 10:37:33 PM

File

UnshufflePermu.pdf
Files produced by the author(s)

Identifiers

Citation

Samuele Giraudo, Stéphane Vialette. Algorithmic and algebraic aspects of unshuffling permutations. Theoretical Computer Science, Elsevier, 2018, 729, pp.20 - 41. ⟨10.1016/j.tcs.2018.02.007⟩. ⟨hal-01797134⟩

Share

Metrics

Record views

119

Files downloads

138