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In this paper, we give a necessary condition for an infinite word defined by a non-degenerate interval exchange on three intervals (3iet word) to be invariant by a substitution: a natural parameter associated to this word must be a Sturm number. We deduce some algebraic consequences from this condition concerning the incidence matrix of the associated substitution. As a by-product of our proof, we give a combinatorial characterization of 3iet words.
We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincare maps of measured foliations a suitable definition of return words which yields that the set of first return words
We prove new results concerning the relation between bifix codes, episturmian words and subgroups offree groups. We study bifix codes in factorial sets of words. We generalize most properties of ordinary maximal bifix codes to bifix codes maximal in
A word $sigma=sigma_1...sigma_n$ over the alphabet $[k]={1,2,...,k}$ is said to be {em smooth} if there are no two adjacent letters with difference greater than 1. A word $sigma$ is said to be {em smooth cyclic} if it is a smooth word and in addition
We extend results regarding a combinatorial model introduced by Black, Drellich, and Tymoczko (2017+) which generalizes the folding of the RNA molecule in biology. Consider a word on alphabet ${A_1, overline{A}_1, ldots, A_m, overline{A}_m}$ in which
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian, this baseline result is used as the basis of existence proofs for universal cycles (also known as generalized deBruijn cycles or U-cycles) of several combinat