Geodesic
The operad of finite labeled tournaments
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2009), pp. 65-75

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We study the operad of finite labeled tournaments. We describe the structure of suboperads of this operad generated by simple tournaments. We prove that a suboperad generated by a tournament with two vertices (i.e., the operad of finite linearly ordered sets) is isomorphic to the operad of symmetric groups, and a suboperad generated by a simple tournament with more that two vertices is isomorphic to the quotient operad of the free operad with respect to a certain congruence. We obtain this congruence explicitly.
Keywords: operad, tournament. 
@article{IVM_2009_2_a4,
     author = {S. N. Tronin and L. T. Abdulmyanova},
     title = {The operad of finite labeled tournaments},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {65--75},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2009_2_a4/}
}
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S. N. Tronin; L. T. Abdulmyanova. The operad of finite labeled tournaments. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2009), pp. 65-75. http://geodesic.mathdoc.fr/item/IVM_2009_2_a4/