Enumerating Possible Seedings in a Knockout Tournament

A knockout tournament, also known as an elimination tournament is a very common competition scheme where competitors play a one-versus-one game with the loser eliminated from the competition and the winner advancing to the next round until there is only one competitor left. The setting of the first round of games called "seeding" naturally influences the competition. Although there is considerable amount of work in the literature on how to seed a knockout tournament to achieve some objectives, an algorithm to enumerate possible knockout tournament seedings has not been explicitly presented to the best of our knowledge. In this paper, a discussion on counting the number of possible seedings in a knockout tournament and an algorithm for effectively enumerating the seedings are proposed.