The Density of Costas Arrays Decays Exponentially

Combinatorics Seminar
Friday, May 28, 2021 - 3:00pm for 1 hour (actually 50 minutes)
Christopher Swanson – Ashland University
Lutz Warnke

Costas arrays are useful in radar and sonar engineering and many other settings in which optimal 2-D autocorrelation is needed: they are permutation matrices in which the vectors joining different pairs of ones are all distinct.
In this talk we discuss some of these applications, and prove that the density of Costas arrays among permutation matrices decays exponentially, solving a core problem in the theory of Costas arrays. 
The proof is probabilistic, and combines ideas from random graph theory with tools from probabilistic combinatorics.

Based on joint work in progress with Bill Correll, Jr. and Lutz Warnke.