UVictoria Discrete Math Seminar: Joy Cooper

A Latin square of order $n$ is an $n\times n$ grid of $n$ symbols each appearing exactly once in every row and column. If we decompose Latin squares by symbol, we can express them as sums of permutation matrices equalling a constant matrix. In this way, the Latin squares of order $n$ span a vector space. We shall provide a brief introduction into the representation theory of the symmetric group in order to bound the dimension of this vector space.