## Factorization forests of finite height.(English)Zbl 0693.68044

We introduce factorization forests. It is shown that the vertex set of a dense factorization forest of finite height satisfies a bounded gap Ramsey-type property of words. The main result is that every morphism from a free semigroup to a finite semigroup S admits a Ramseyan factorization forest of height at most $$9| S|$$. Technique for constructing factorization forests are developed.
Reviewer: Imre Simon

### MSC:

 68Q45 Formal languages and automata 05A10 Factorials, binomial coefficients, combinatorial functions 68R99 Discrete mathematics in relation to computer science
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### References:

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