Vol. 12, No. 6, 2019

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Sidon sets and 2-caps in $\mathbb{F}_3^n$

Yixuan Huang, Michael Tait and Robert Won

Vol. 12 (2019), No. 6, 995–1003
Abstract

For each natural number d, we introduce the concept of a d-cap in F3n. A set of points in F3n is called a d-cap if, for each k = 1,2,,d, no k + 2 of the points lie on a k-dimensional flat. This generalizes the notion of a cap in F3n. We prove that the 2-caps in F3n are exactly the Sidon sets in F3n and study the problem of determining the size of the largest 2-cap in F3n.

Keywords
Sidon sets, cap sets, caps, 2-caps
Mathematical Subject Classification 2010
Primary: 05B10, 05B25, 05B40, 51E15
Milestones
Received: 16 September 2018
Revised: 7 February 2019
Accepted: 18 February 2019
Published: 3 August 2019

Communicated by Joshua Cooper
Authors
Yixuan Huang
Department of Mathematics and Statistics
Wake Forest University
Winston-Salem, NC
United States
Michael Tait
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA
United States
Robert Won
Department of Mathematics
University of Washington
Seattle, WA
United States