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It is undecidable whether the growth rate of a given bilinear system is 1
Matthieu Rosenfeld
We show that there exists no algorithm that decides for any bilinear system if the growth rate of is . This answers a question of Bui who showed that if the coef…
The growth rate over trees of any family of set defined by a monadic second order formula is semi-computable
Matthieu Rosenfeld
Monadic second order logic can be used to express many classical notions of sets of vertices of a graph as for instance: dominating sets, induced matchings, perfect codes, independ…
How far away must forced letters be so that squares are still avoidable?
Matthieu Rosenfeld
We describe a new non-constructive technique to show that squares are avoidable by an infinite word even if we force some letters from the alphabet to appear at certain occurrences…
Avoidability of long -abelian repetitions
Michaël Rao, Matthieu Rosenfeld
We study the avoidability of long -abelian-squares and -abelian-cubes on binary and ternary alphabets. For , these are Mäkelä's questions. We show that one cannot avoid…