Dot product chains

2020/06/20 by Shelby Kilmer, Kilmer, Shelby, Caleb Marshall +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · #14-3-3 protein interactions

paper · pdf · doi:10.48550/arxiv.2006.11467

Abstract

We study a variant of Erd\H os' unit distance problem, concerning dot products between successive pairs of points chosen from a large finite point set. Specifically, given a large finite set of n points E, and a sequence of nonzero dot products (α₁,…,α_k), we give upper and lower bounds on the maximum possible number of tuples of distinct points (A₁,…, A_k+1)∈ E^k+1 satisfying A_j ⋅ A_j+1=α_j for every 1≤ j ≤ k.

Cited by

• A Density Condition on Point Sets with Slowly-Scaling Distinct Dot Products

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