On a conjecture of Brualdi and Shen on block transitive tournaments

The following conjecture of Brualdi and Shen is proven in this paper: let n be partitioned into natural numbers no one of which is greater than (n + 1) - 2. Then, given any sequence of wins for the players of some tournament among n players, there is a partition of the players into blocks with cardinalities given by those numbers, and a tournament with the given sequence of wins, that is transitive on the players within each block. © 2003 Wiley Periodicals, Inc. J Graph Theory 44: 215–230, 2003