Sequences with constant number of return words

2006/08/24 by Balkova, Lubomira, Pelantova, Edita, Steiner, Wolfgang · 1 citation
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0608603

Abstract

An infinite word has the property R_m if every factor has exactly m return words. Vuillon showed that R₂ characterizes Sturmian words. We prove that a word satisfies R_m if its complexity function is (m-1)n+1 and if it contains no weak bispecial factor. These conditions are necessary for m=3, whereas for m=4 the complexity function need not be 3n+1. New examples of words satisfying R_m are given by words related to digital expansions in real bases.

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