## Colloquium: “Latin squares and their completions”

Marshall University Math Colloquium
October 1, 2014

Dr. Michael Schroeder
Marshall University

Abstract
If you’ve even finished a Sudoku puzzle, then you’ve seen a “completed” latin square. A latin square is an array of symbols where each symbol appears exactly once in each row and each column. A solution to a Sudoku puzzle is a latin square, with the additional constraint of having no repeated symbol in each $3\times 3$ block. Although Sudoku has only been popular for the past decade, mathematicians have been studying latin squares since the 18th century, and have many applications including coding theory and experimental design. We will begin by discussing a brief exposition of latin squares. Then we will go over some properties of latin squares and some classical results identifying when partial latin squares can be completed. To finish, we will talk about some recent results in the field. The beginning of the talk should be very accessible, and toward the end there will be some technical discussion.