Combinatorical and Algebraic Structures Seminar
Session details
| Date: | 23.10.2007 |
| Speaker: | Edita Pelantová, FJFI, České vysoké učení technické |
| Title: | Sequences with a constant number of return words |
| Abstract: | An infinite word has the property $R_m$ if every factor has exactly $m$ return words. Vuillon showed that $R_2$ 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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