Asymptotic enumeration of Latin Rectangles

Abstract

Latin rectangles are among the oldest objects in combinatorics, yet their enumeration has resisted precise analysis. In recent joint work with Ledecky and Wormald, we develop asymptotics for their number, using methods that we first designed for counting regular graphs of medium density. The key idea is to build a probability space where point probabilities can be evaluated with high accuracy - revealing the normalized count of Latin rectangles as one such probability. The talk will be introductory in nature.