## Density of Sequences with Forbidden Separations

- April 27, 2018
- 2:30 p.m.
- LeConte 312

## Abstract

Fix a set D of positive integers. A D-sequence is an integral sequence so that the difference between any two elements in the sequence does not fall in D. The maximum density of a D-sequence is denoted by m(D). Introduced by Cantor and Gordon in the mid-70’s, the parameter m(D) is closely related to many problems studied in different fields. For instance, Griggs and Liu proved that m(D) is closely related to the channel assignment problem for mutually adjacent cites when the interference set is D. In this talk, we introduce relations of m(D) to the coloring parameters of distance graphs (initiated by Eggleton, Erӧds, and Skilton in the mid-80’s from the plane coloring problem) and the parameter involved in the so call “lonely runner conjecture”. In addition, we survey results on applications of these relations and recent works on m(D).