Embedding a θ-invariant code into a complete one

01/16/2018

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by   Jean Néraud, et al.

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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].