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Pré-Publication, Document De Travail Année : 2018

Embedding a θ-invariant code into a complete one

Résumé

Let A be a finite or countable alphabet and let θ be a literal (anti)morphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under θ (θ-invariant for short). We establish a formula which allows to embed any non-complete θ-invariant code into a complete one: this brings a positive answer to the open question that was stated in [[Néraud J. and Selmi C. Invariance: a theoretical approach for coding sets of words modulo literal (anti)morphisms. In S. Brlek, F. Dolce, C. Reutenauer, and E. Vandomme, editors, Combinatorics on Words, volume 10432, pages 214-227. Lect. Notes in Comp. Sci., sept 2017].
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Dates et versions

hal-01683320 , version 1 (15-01-2018)
hal-01683320 , version 2 (11-08-2018)
hal-01683320 , version 3 (31-08-2018)

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Jean Néraud, Carla Selmi. Embedding a θ-invariant code into a complete one. 2018. ⟨hal-01683320v1⟩
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