Whirlwind Tour
of Math

Fall 2007

Latin Squares

Latin squares is where I spend most of my time when I'm playing in mathland (that is, doing research math). To push the whirlwind tour metaphor a step too far, you could probably describe the theory of Latin squares as an unfashionable suburb of a medium-sized city called Combinatorics. Desptite this description, there are some neat bits of math if you know where to look, and I enjoy living there.
So what is a Latin square? It's a grid of numbers that obey various rules. You can find a bit more detail here. One example you are probably familiar with is sudoku. A completed sudoku puzzle is a 9 by 9 Latin square.
There are many natural questions to ask that can be surprisingly tricky to answer (How many Latin squares of a given size are there? What if we restrict with special rules, like sudoku does?) There are also some interesting applications ranging from the design of scientific experiments to the construction of efficient codes.
http://cs.marlboro.edu/ courses/ fall2007/math_tour/ lsq
last modified Monday October 1 2007 8:55 am EDT