Geodesic
Operads of Decorated Cliques II: Noncrossing Cliques
Séminaire lotharingien de combinatoire, Tome 79 (2018-2023)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

A complete study of an operad NCM of noncrossing configurations of chords introduced in previous work of the author is performed. This operad is defined on the linear span of all noncrossing M-cliques. These are noncrossing configurations of chords with arcs labeled by a unitary magma M. The magmatic product of M intervenes for the computation of the operadic composition of M-cliques. We show that this operad is binary, quadratic, and Koszul by considering techniques coming from rewrite systems on trees. We also compute a presentation for its Koszul dual. Finally, we explain how NCM allows one to obtain alternative constructions of already known operads like operads of formal fractions and the operad of bicolored noncrossing configurations. 

@article{SLC_2018-2023_79_a7,
     author = {Samuele Giraudo},
     title = {Operads of {Decorated} {Cliques} {II:} {Noncrossing} {Cliques}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {79},
     year = {2018-2023},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a7/}
}
TY  - JOUR
AU  - Samuele Giraudo
TI  - Operads of Decorated Cliques II: Noncrossing Cliques
JO  - Séminaire lotharingien de combinatoire
PY  - 2018-2023
VL  - 79
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a7/
ID  - SLC_2018-2023_79_a7
ER  - 
%0 Journal Article
%A Samuele Giraudo
%T Operads of Decorated Cliques II: Noncrossing Cliques
%J Séminaire lotharingien de combinatoire
%D 2018-2023
%V 79
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a7/
%F SLC_2018-2023_79_a7
Samuele Giraudo. Operads of Decorated Cliques II: Noncrossing Cliques. Séminaire lotharingien de combinatoire, Tome 79 (2018-2023). http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a7/