Compact packings of the plane with discs

Abstract: After explaining what a compact packing of the plane by discs is, I will discuss the following question: "For which $n$-tuples of distinct positive real numbers is there a compact packing of the plane with discs, so that, firstly, only the mentioned $n$ numbers are used as radii of discs in the packing, and secondly, every one of the mentioned $n$ numbers occurs at least once as a radius of a disc in the packing?"

I will discuss some aspects of this question along with its history, which is surprisingly recent (e.g., the case $n=2$ was only solved in 2006).

combinatorics

Audience: researchers in the topic

Warwick Combinatorics Seminar

Series comments: This is the online combinatorics seminar at Warwick.