circular chains of chinese dice

      In this paper we study Chinese dice, mathematical objects similar to ordinary dice but allowing repetition among their face values.We say that a die A is preferred over a die B (written A B) if A wins more frequently than B does. We study first the existence of circular chains of three dice A,...

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Autores Principales: Piza Volio, Eduardo, Schubert, Leo
Formato: Artículo
Idioma: Español
Publicado: 2015
Acceso en línea: http://revistas.ucr.ac.cr/index.php/matematica/article/view/312
http://hdl.handle.net/10669/12970
Sumario:       In this paper we study Chinese dice, mathematical objects similar to ordinary dice but allowing repetition among their face values.We say that a die A is preferred over a die B (written A B) if A wins more frequently than B does. We study first the existence of circular chains of three dice A, B, C (those that A B C > A) using a mixed integer programming algorithm. Then we generalize the problem to n-dimensional dice—that is, dice of n faces, with n ? 4—and we search circular chains of length m (with m ? 3) using a simulated annealing algorithm. We compare some different objective functions and obtain good solutions to the problem with very efficient algorithms. Finally we obtain a theoretical result concerning the existence of circular chains in the general case.