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The operad of finite labeled tournaments

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Abstract

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.

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Authors and Affiliations

  1. Kazan State University, ul. Kremlyovskaya 18, Kazan, 420008, Russia

    S. N. Tronin & L. T. Abdulmyanova

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  1. S. N. Tronin
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  2. L. T. Abdulmyanova
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Correspondence to S. N. Tronin.

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Original Russian Text © S.N. Tronin, L.T. Abdulmyanova, 2009, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, No. 2, pp. 65–75.

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Tronin, S.N., Abdulmyanova, L.T. The operad of finite labeled tournaments. Russ Math. 53, 59–67 (2009). https://doi.org/10.3103/S1066369X09020054

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  • DOI: https://doi.org/10.3103/S1066369X09020054

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