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Generalizations of the associative operad and convergent rewrite systems

EasyChair Preprint 143

6 pagesDate: May 18, 2018

Abstract

The 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

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
@booklet{EasyChair:143,
  author    = {Cyrille Chenavier and Christophe Cordero and Samuele Giraudo},
  title     = {Generalizations of the associative operad and convergent rewrite systems},
  doi       = {10.29007/mfnh},
  howpublished = {EasyChair Preprint 143},
  year      = {EasyChair, 2018}}
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