When do Latin squares have orthogonal mates?

Series
Combinatorics Seminar
Time
Friday, August 23, 2024 - 3:15pm for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Candy Bowtellhttps://sites.google.com/view/candidabowtell
Organizer
Tom Kelly

A Latin square is an nxn grid filled with n symbols such that each symbol appears exactly once in each row and column. A transversal in a Latin square is a collection of n cells such that each row, column and symbol appears exactly once in the collection.

Latin squares were introduced by Euler in the 1700s and he was interested in the question of when a Latin square decomposes fully into transversals. Equivalently, when does a Latin square have an 'orthogonal mate'?

We'll discuss the history of this question, and some upcoming joint work with Richard Montgomery.