## Combinatorics on words |

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### Contents

Words by Dominique Perrin | 1 |

SquareFree Words and Idempotent Semigroups | 18 |

Van der Waerdens Theorem by Jean Eric Pin | 39 |

Copyright | |

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ala2 algorithm alphabet antichain arithmetic progression assume bijection binomial coefficients Chapter combinatorial commutative condition congruence conjugate consider construction contains Corollary critical factorization cyclic root Deduce defined definition denoted disjoint dominated circuit elements equal equation equivalent Example exists a unique exists an integer Foata formal power series free group free Lie algebra free monoid free submonoid given Hence holds idempotent identity implies induction hypothesis infinite square-free words infinite word integer inverse Lemma letter lexicographic order Lyndon words mapping mathematics matrix minimal modulo morphism nonempty word notation obtain overlapping factor pair parametric word permutation polynomial positive integer principal solution Problem proper right factor Proposition prove quotient monoid rearrangement relation resp result satisfies Schutzenberger Section semigroup sequence set of words Show shuffle ideals submodule submonoid subset subword theory totally ordered tree verifies Viennot Waerden's theorem word h words of length