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Contextual partial commutations

Abstract : We consider the monoid T with the presentation < a, b; aab = aba > which is ''close'' to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid \a, b\* and solve the classical equations, such as commutation and conjugacy in T. Then we study the closure properties of the two subfamilies of the rational subsets of T whose lexicographically minimum and maximum cross-sections respectively, are rational in \a, b\*.
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Christian Choffrut, Robert Mercas. Contextual partial commutations. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2010, 12 (4), pp.59-72. ⟨hal-00990446⟩

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