Download PDFOpen PDF in browserGeneralizations of the associative operad and convergent rewrite systemsEasyChair Preprint 1436 pages•Date: May 18, 2018AbstractThe associative operad is the quotient of the magmatic operad by the operad congruence identifying the two binary trees of degree $2$. We introduce here a generalization of the associative operad depending on a nonnegative integer $d$, called $d$-comb associative operad, as the quotient of the magmatic operad by the operad congruence identifying the left and the right comb binary trees of degree $d$. We study the case $d = 3$ and provide an orientation of its space of relations by using rewrite systems on trees and the Buchberger algorithm for operads to obtain a convergent rewrite system. Keyphrases: Associative operad, Buchberger algorithm, Operad, combinatorics, rewrite system, tree
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