A contribution to the mathematical theory of tournaments, using the probabilistic method and the notation of J. W. Moon, [Topics in Tournaments]. This paper shows how to prove properties of a random element of the class of regular tournaments. It presents and proves a theorem giving a bound on the number of tournaments with a given score sequence; shows how random regular tournaments act "locally" like random tournaments; proves a theorem on partial order contained in tournaments; finds bounds on the number of regular tournaments in both the labeled and the unlabeled cases; and determines the number of non-isomorphic regular tournaments with odd and even number of players. 34 pp. Ref.
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