Generalizations of the associative operad and convergent rewrite systems

## Authors: Cyrille Chenavier, Christophe Cordero and Samuele Giraudo

## Paper Information

Title: | Generalizations of the associative operad and convergent rewrite systems |

Authors: | Cyrille Chenavier, Christophe Cordero and Samuele Giraudo |

Proceedings: | HDRA Abstracts |

Editors: | Samuel Mimram, Yves Guiraud and Philippe Malbos |

Keywords: | Operad, Tree, Rewrite system, Combinatorics, Associative operad, Buchberger algorithm |

Abstract: | 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. |

Pages: | 6 |

Talk: | Jul 07 17:00 (Session 31D) |

Paper: |