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| Title: | Permutads |
| Authors: | Loday, J.L.
Ronco, M. |
| Keywords: | Tree
Permutohedron
Permutad
Operad
Shuffle
Weak Bruhat order |
| Issue Date: | Feb-2013 |
| Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA |
| Citation: | JOURNAL OF COMBINATORIAL THEORY SERIES A Volume: 120 Issue: 2 Pages: 340-365 DOI: 10.1016/j.jcta.2012.08.005 |
| Abstract: | We unravel the algebraic structure which controls the various ways of computing the word ((xy)(zt)) and its siblings. We show that it gives rise to a. new type of operads, that we call permutads. A permutad is an algebra over the monad made of surjective maps between finite sets. It turns out that this notion is equivalent to the notion of "shuffle algebra" introduced previously by the second author. It is also very close to the notion of "shuffle operad" introduced by V. Dotsenko and A. Khoroshkin. It can be seen as a noncommutative version of the notion of nonsymmetric operads. We show that the role of the associahedron in the theory of operads is played by the permutohedron in the theory of permutads. (C) 2012 Elsevier Inc. All rights reserved. |
| Description: | Loday, JL (Loday, Jean-Louis); Ronco, M (Ronco, Maria)[ 1 ] Univ Talca, Inst Matemat & Fis, Santiago, Chile. |
| URI: | http://dspace.utalca.cl/handle/1950/9495 |
| ISSN: | 0097-3165 |
| Appears in Collections: | Artículos en publicaciones ISI - Universidad de Talca
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