Combinatorics Seminar

On the number of discrete chains

Eyvindur Palsson, Virginia Tech University

Thursday, November 7th, 2019
11:00 AM - 12:00 PM
Hylan 1106A

One of Erdos’ greatest contributions to geometry was his problem on distinct distances where he asked: what is the least number of distinct distances among N points? This seemingly innocent question inspired many other related questions, such as the Erdos unit distance problem, which asks: how often can a particular distance at most arise among N points? In this talk we will recount the history of these questions and then focus on a new result that studies a generalization of the Erdos unit distance problem to chains of k distances. In particular, given P, a set of N points, and a sequence of distances $(\delta_1,\ldots,\delta_k)$, we study the maximum possible number of tuples of distinct points $(p_1,\ldots,p_{k+1})$ in $P^{k+1}$ satisfying $\vert p_j-p_{j+1}\vert=\delta_j$ for every $1\leq j \leq k$. We derive upper and lower bounds for this family of problems.

Event contact: hazel dot mcknight at rochester dot edu