14 citations · 54 across the 28 of their papers we have counts for
10 papers · 1 filter
On extended boundary sequences of morphic and Sturmian words
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the th term of the -boundary sequence of an infinite word is the finite set of pairs o…
Characterizations of families of morphisms and words via binomial complexities
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Two words are -binomially equivalent if each subword of length at most occurs the same number of times in both words. The -binomial complexity of an infinite word is a co…
The carry propagation of the successor function
Valérie Berthé, Christiane Frougny, Michel Rigo +1
Given any numeration system, we call carry propagation at a number the number of digits that are changed when going from the representation of to the one of , and amor…
Counting Subwords Occurrences in Base-b Expansions
Julien Leroy, Michel Rigo, Manon Stipulanti
We count the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. More precisely, we consider the sequence co…
Counting the number of non-zero coefficients in rows of generalized Pascal triangles
Julien Leroy, Michel Rigo, Manon Stipulanti
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomia…
Generalized Pascal triangle for binomial coefficients of words
Julien Leroy, Michel Rigo, Manon Stipulanti
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 ano…
Asymptotic properties of free monoid morphisms
Emilie Charlier, Julien Leroy, Michel Rigo
Motivated by applications in the theory of numeration systems and recognizable sets of integers, this paper deals with morphic words when erasing morphisms are taken into account.…
Invariant games and non-homogeneous Beatty sequences
Julien Cassaigne, Eric Duchêne, Michel Rigo
We characterize all the pairs of complementary non-homogenous Beatty sequences and for which there exists an invariant game having exactly $\{(A_n…
Multidimensional extension of the Morse--Hedlund theorem
Fabien Durand, Michel Rigo
A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence over a finite alphabet is ultimately periodic if and only if, for some , the number of diff…
Syndeticity and independent substitutions
Fabien Durand, Michel Rigo
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 define the no…