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Asma Paracha, December 12, 2017, 15:30-16:00, ITB 201
Speaker:   Asma Paracha

Title:  Lyndon factors and periodicities in strings
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Alexander Rosa, December 12, 2017, 16:30-17:30, ITB 201
Speaker:   Alexander Rosa
Department of Mathematics & Statistics
McMaster University

Title:  Reaction graphs of combinatorial configurations
Fields Institute Industrial Optimization Seminar, November 14, 2017
Speakers:   Christopher Swartz (McMaster University)
Jesus Flores-Carrillo (Praxair)

On the first Tuesday of each month, the Industrial Optimization Seminar is held at the Fields Institute. See the seminar series website for further information.
Home arrow Seminars arrow Invited seminars arrow Dalibor Froncek, September 25, 2013, 16:30-17:30, ITB 201
Friday, 24 November 2017
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Dalibor Froncek, September 25, 2013, 16:30-17:30, ITB 201
Speaker:   Dalibor Froncek
Department of Mathematics and Statistics
University of Minnesota Duluth

Title:  Incomplete round robin tournaments, graph labelings, and magic rectangle sets

Suppose you have a league of n teams that are ranked 1,2,…,n based on their standings in the previous year. If you want them to play a complete round robin tournament, then the last year's winner will apparently have the easiest schedule (they do not play against the strongest team – themselves) and so on, while the weakest team will have the most difficult schedule. What happens when you do not have enough time to play the complete tournament? Maybe you can only schedule g<n-1 games per team. Can you mimic the complete tournament? That is, can you schedule it so that the strongest team has the easiest schedule, while the weakest team has the hardest one? It is easy to see that this is equivalent to scheduling of a tournament with n-1-g games per team, in which the "strength of schedule" (that is, the sum of rankings of the team's opponents) will be the same for each team. We will use graph labelings to show when it is possible to schedule such a tournament. Many of them are based on magic rectangles. However, the most interesting tournament is an incomplete handicap tournament, in which the chances of winning would be the same for each team. In such a tournament the strongest team would have the most difficult schedule, while the weakest team would have the easiest one. We will show such tournaments, whose construction is based on a generalization of magic rectangles, namely magic rectangle sets.
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