Discrete Mathematics & Theoretical Computer Science, Vol 12, No 4 (2010)

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Contextual partial commutations

Christian Choffrut, Robert George Mercaş


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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