Abstract : k-abelian singletons in connection with Gray codes for Necklaces. This work is based on [1]. We are interested in the equivalence classes induced by k-abelian equivalence, especially in the number of the classes containing only one element, k-abelian singletons. By characterizing k-abelian equivalence with k-switchings, a sort of rewriting operation, we are able to obtain a structural representation of k-abelian singletons. Analyzing this structural result leads, through rather technical considerations, to questions of certain properties of sets of vertex-disjoint cycles in the de Bruijn graph dBΣ(k−1) of order k−1. Some problems turn out to be equivalent to old open problems such as Gray codes for necklaces (or conjugacy classes). We shall formulate the problem in the following. [...]
Recording during the thematic meeting: « Combinatorics on Words
» the March 16, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France)
Filmmaker: Guillaume Hennenfent
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Markus Whiteland : k-abelian singletons and Gray codes for Necklaces cnrs montpellier | |
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