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Generalized Pascal triangle for binomial coefficients of words Leroy, Julien ; Rigo, Michel ; Stipulanti, Manon in Advances in Applied Mathematics (2016), 80 We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word ... [more ▼] We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of another finite word. Similarly to the Sierpiński gasket that can be built as the limit set, for the Hausdorff distance, of a convergent sequence of normalized compact blocks extracted from Pascal triangle modulo 2, we describe and study the first properties of the subset of [0, 1] × [0, 1] associated with this extended Pascal triangle modulo a prime p. [less ▲] Detailed reference viewed: 47 (26 ULg)Factor Complexity of S-adic words generated by the Arnoux-Rauzy-Poincaré Algorithm Labbé, Sébastien ; in Advances in Applied Mathematics (2015), 63 Detailed reference viewed: 7 (0 ULg)Some improvements of the S-adic conjecture Leroy, Julien in Advances in Applied Mathematics (2012), 48(1), 79--98 Detailed reference viewed: 17 (3 ULg)Syndeticity and independent substitutions ; Rigo, Michel in Advances in Applied Mathematics (2009), 42 We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we de ne the notion of two independent ... [more ▼] We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we de ne the notion of two independent substitutions. Our main result is the following. If a sequence x is generated by two independent substitutions, at least one being of exponential growth, then the factors of x appearing in nitely often in x appear with bounded gaps. As an application, we derive an analogue of Cobham's theorem for two independent substitutions (or abstract numeration systems) one with polynomial growth, the other being exponential. [less ▲] Detailed reference viewed: 50 (11 ULg) |
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