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Compressions: A Tale of Love and Two Rings

UW OSHKOSH MATHEMATICS DEPARTMENT COLLOQUIUM
When Apr 23, 2014
from 04:00 PM to 05:00 PM
Where Swart 217
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Dr. Kenneth Price, Professor of Mathematics

Wednesday, April 23, 2014 Swart 217 from 4:00 to 5:00 pm

 

With springtime come thoughts of love and gardens. These thoughts are linked in Louise Riottes gardening book, Carrots Love Tomatoes, which points out carrots tend to be healthier when planted near tomatoes. On the other hand, potatoes do not love tomatoes because they share diseases.

To design gardens with happy plants in mind, we use directed graphs to show love from plant to plant. If plant A loves plant B we draw an arrow pointing from A to B:

Even though potatoes love cabbages and cabbages love tomatoes, potatoes do not love tomatoes. Thus love is not always transitive and this must be accounted for in a garden plan. Many graph-lovers would add all arrows forced by transitivity, but here this would be a mistake: these extra arrows in the transitive closure of a garden may lie about love.

But do not despair. We present a transitive closure alternative, which may appeal to gardeners and, as well see, also has interesting applications to matrices.

by Kuennen, Eric W last modified Apr 11, 2014 01:31 PM

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