For more information about this meeting, contact Matthew Katz, James Sellers, George Andrews.
| Title: | Periodic billiard paths and integer partitions |
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| Seminar: | Combinatorics/Partitions Seminar |
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| Speaker: | Andrew Baxter, PSU |
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| Abstract: |
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| Throw a ball on a polygonal billiard table and it will trace a path
dictated by the laws of reflection. If the path loops back on itself
after n bounces, we call it a period-n billiard path. For a given
polygon, we are interested in counting all period-n billiard paths (up
to a natural equivalence relation). We will focus on the cases of the
rectangle, square, right isosceles triangle, and 30-60-90 triangle.
In the course of doing this, we will run across a geometric
interpretation of Euler's totient function and develop an intriguing
connection with integer partitions which hints at a much richer
structure than one would suspect. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 11 / 08 / 2011 |
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| Time: | 11:15am - 12:05pm |
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