Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Number Theory Seminar


Monday, March 16th, 2020

Time: 4:30-5:30 p.m.  Place: Jeffery Hall 422

Speaker: Keshia Yap

Title: Dimension of magic squares over a field.

Abstract: In this talk, we will follow the proof of Charles Small's 1988 paper to compute the dimension of magic squares over fields. A magic square of size $n$ over a field $F$ is an $n \times n$ matrix for which every row, every column, the principal diagonal and the principal backdiagonal all have the same sum. The set of all magic squares is an $F$-vector space. We will prove that for $n \geq 5$, its dimension is $n^2 - 2n$ (for all $F$), and for $n