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- Centre National de la Recherche ScientifiqueFR676 papers
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5 papers · 2 filters
On additive properties of sets defined by the Thue-Morse word
Michelangelo Bucci, Neil Hindman, Svetlana Puzynina +1
In this paper we study some additive properties of subsets of the set $\nats$ of positive integers: A subset of $\nats$ is called {\it -summable} (where $k\in\ben$) if c…
Weak abelian periodicity of infinite words
Sergey Avgustinovich, Svetlana Puzynina
We say that an infinite word w is weak abelian periodic if it can be factorized into finite words with the same frequencies of letters. In the paper we study properties of weak abe…
On a generalization of Kelly's combinatorial lemma
Aymen Ben Amira, Jamel Dammak, Hamza Si Kaddour
Kelly's combinatorial lemma is a basic tool in the study of Ulam's reconstruction conjecture. A generalization in terms of a family of t-elements subsets of a v-element set was giv…
Central sets and substitutive dynamical systems
Marcy Barge, Luca Q. Zamboni
In this paper we establish a new connection between central sets and the strong coincidence conjecture for fixed points of irreducible primitive substitutions of Pisot type. Centra…
On a generalization of Abelian equivalence and complexity of infinite words
Juhani Karhumaki, Aleksi Saarela, Luca Q. Zamboni
In this paper we introduce and study a family of complexity functions of infinite words indexed by $k \in \ints ^+ \cup {+\infty}.$ Let $k \in \ints ^+ \cup {+\infty}$ and be a…