Abstract
We construct, via usual graph theory a class of associative dialgebras as well as a class of coassociative L-coalgebras, the two classes being related by a tool from graph theory called the line-extension. As a corollary, a tiling of the n 2-De Bruijn graph with n (geometric supports of) coassociative coalgebras is obtained. Via the tiling of the (3, 1)-De Bruijn graph, we also get an example of cubical trialgebra, notion introduced by Loday and Ronco. Other examples are obtained by letting M n (k) act on axioms defining such tilings. Examples of associative products which split into several associative ones are also given.
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