%0 Journal Article %A Choffrut, Christian %A Mercas, Robert %D 2017 %T Contextual partial commutations %U https://repository.lboro.ac.uk/articles/journal_contribution/Contextual_partial_commutations/9402023 %2 https://repository.lboro.ac.uk/ndownloader/files/17018588 %K Contextual trace monoids %K Partial commutations %K Information and Computing Sciences not elsewhere classified %X We consider the monoid T with the presentation 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}*. © 2010 Discrete Mathematics and Theoretical Computer Science. %I Loughborough University