Please Join the Mathematics Department for a Colloquium for General Audiences

Enumeration of Magic Squares

By

William Griffiths, Ph. D.

SPSU Mathematics Department

Thursday, October 6, 2005

3 pm D219

Cookies at 2:45 pm

> A magic square is an n x n matrix with non-negative integer entries, > such that the sum of the entries in each row and column (called the line > sum) is the same. There are two ways to consider these objects: > hold the line sum fixed and vary the size of the matrix; > alternatively, fix the size of the matrix and vary the line > sum. Although a good deal is known if we fix the size of the matrix > and vary the sum, there are still many questions to be answered for > fixed line sum. What proofs we have are far from “proofs from > the Book,” spoken of by the late, great Paul Erdos.>

> The magic squares of line sum 1 are equivalent to permutations. We will > attempt to use permutations to view magic squares of larger line sum in > a new light. We will emphasize proofs using as few high powered tools > as possible, instead relying on counting argument. Some new results > will be discussed, as well as possible avenues for future research.

Come enjoy an afternoon of playing with regular old whole numbers!