| DATE: | Thursday, November 8, 2001 |
| TIME: | 4:30-5:30 PM |
| PLACE: | LN 2205 |
| SPEAKER: | Mattias Beck (Binghamton University) |
| TITLE: | On the number of "magic squares" |
Define a magic square as an n-by-n matrix whose nonnegative integer entries add up to the same integer t in each row, column, and main diagonal. We study the number of such square arrays as a function of t. Geometrically, this amounts to counting integer points in a polytope defined by the linear system of the magic-square constraints. This geometric interpretation allows us to derive structural results about our counting function. These techniques extend easily to other settings, for example, "magic" hypercubes. Finally, we present a complex-analytic way of computing counting functions such as the above, and connect these functions to some famous unsolved problems on polytopes.