On the Number of Dot Product Chains in Finite Fields and Rings

Authors

• Vincent Blevins, Missouri State University
• David Crosby, Missouri State University
• Ethan Lynch, Missouri State University
• Steven Senger, Missouri State UniversityFollow

Abstract

We explore variants of Erd?s’ unit distance problem concerning dot products between successive pairs of points chosen from a large finite subset of either Fqd or Zqd, where q is a power of an odd prime. Specifically, given a large finite set of points E, and a sequence of elements of the base field (or ring) (?1, …, ?k), we give conditions guaranteeing the expected number of (k+ 1 ) -tuples of distinct points (x1, ?, xk+1) ? E^k+1 satisfying xj· xj+1= ?j for every 1 ? j? k.

Department(s)

Mathematics

Document Type

Conference Proceeding

DOI

10.1007/978-3-031-10796-2_1

Publication Date

1-1-2022

Recommended Citation

Blevins, Vincent; Crosby, David; Lynch, Ethan; and Senger, Steven, "On the Number of Dot Product Chains in Finite Fields and Rings" (2022). Faculty Scholarship. 796.
https://bearworks.missouristate.edu/articles00/796

Journal Title

Springer Proceedings in Mathematics and Statistics