We define new combinatorial objects, called shrubs, such that forests of rooted trees are shrubs. We then introduce a structure of operad on shrubs. We show that this operad is contained in the Zinbiel operad, by using the inclusion of Zinbiel in the operad of moulds. We also prove that this inclusion is compatible with the richer structure of anticyclic operad that exists on Zinbiel and on moulds.
Mot clés : Opérade, opérade anticyclique, arbre, permutation, fraction
Mots clés : Operad, anticyclic operad, tree, permutation, fraction
Frédéric Chapoton 1
@article{AMBP_2010__17_1_17_0,
author = {Fr\'ed\'eric Chapoton},
title = {Une op\'erade anticyclique sur les arbustes},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {17--45},
publisher = {Annales math\'ematiques Blaise Pascal},
volume = {17},
number = {1},
year = {2010},
doi = {10.5802/ambp.277},
mrnumber = {2674653},
zbl = {1202.18005},
language = {fr},
url = {https://ambp.centre-mersenne.org/articles/10.5802/ambp.277/}
}
TY - JOUR AU - Frédéric Chapoton TI - Une opérade anticyclique sur les arbustes JO - Annales mathématiques Blaise Pascal PY - 2010 SP - 17 EP - 45 VL - 17 IS - 1 PB - Annales mathématiques Blaise Pascal UR - https://ambp.centre-mersenne.org/articles/10.5802/ambp.277/ DO - 10.5802/ambp.277 LA - fr ID - AMBP_2010__17_1_17_0 ER -
%0 Journal Article %A Frédéric Chapoton %T Une opérade anticyclique sur les arbustes %J Annales mathématiques Blaise Pascal %D 2010 %P 17-45 %V 17 %N 1 %I Annales mathématiques Blaise Pascal %U https://ambp.centre-mersenne.org/articles/10.5802/ambp.277/ %R 10.5802/ambp.277 %G fr %F AMBP_2010__17_1_17_0
Frédéric Chapoton. Une opérade anticyclique sur les arbustes. Annales mathématiques Blaise Pascal, Tome 17 (2010) no. 1, pp. 17-45. doi : 10.5802/ambp.277. https://ambp.centre-mersenne.org/articles/10.5802/ambp.277/
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