# Codes and Expansions (CodEx) Seminar

## Lutz Warnke (University of California San Diego)The Density of Costas Arrays Decays Exponentially

Costas arrays arise in radar and sonar engineering applications: formally they are simply permutation matrices in which the vectors joining different pairs of ones are all distinct. It is natural to ask how many Costas arrays there are, and we shall prove that the density of Costas arrays among permutation matrices decays exponentially. Perhaps surprisingly, the proof uses ideas from random graph theory and probabilistic combinatorics. The talk is aimed at a general audience.

Based on joint work with Bill Correll, Jr (Maxar Technologies) and Christopher Swanson (Ashland University).