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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 2, Pages 65–75
(Mi ivm1262)
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The operad of finite labeled tournaments
S. N. Tronin, L. T. Abdulmyanova Kazan State University
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.
Keywords:
operad, tournament.
Received: 22.11.2006 Revised: 02.07.2007
Citation:
S. N. Tronin, L. T. Abdulmyanova, “The operad of finite labeled tournaments”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 2, 65–75; Russian Math. (Iz. VUZ), 53:2 (2009), 59–67
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https://www.mathnet.ru/eng/ivm1262 https://www.mathnet.ru/eng/ivm/y2009/i2/p65
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Abstract page: | 397 | Full-text PDF : | 71 | References: | 56 | First page: | 4 |
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