Northern Michigan University, Mathematics, Marquette, MI 49855
If you are the organizer of your local sports team, you will need to coordinate a schedule. Whether you have 20 teams, 50 teams, or n teams… we have a solution. Suppose there are n teams, each team playing a team just once, not considering whether games are at home or away. If n is even, we have n-1 rounds with n/2 games in each round. If n is odd, we use a dummy team who acts a bye week. When n is odd we have n rounds with (n-1)/2 games in each round. To set up a schedule, the round robin algorithm can be used. In this talk our goal is not to find a schedule, instead we are interested in finding how many ways there are to set up a schedule. Through the use of the round robin algorithm we have a solution with a lower and upper bound.
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