Embedding distance graphs in finite field vector spaces

2018/02/18 by Alex Iosevich, Iosevich, Alex, Hans Parshall +1
Computer Science · Mathematics · #52C10 #Classical Analysis and ODEs (math.CA) #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1802.06460

openalex publication_date 2018/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that large subsets of vector spaces over finite fields determine certain point configurations with prescribed distance structure. More specifically, we consider the complete graph with vertices as the points of A ⊆ F_q^d and edges assigned the algebraic distance between pairs of vertices. We prove nontrivial results on locating specified subgraphs of maximum vertex degree at most t in dimensions d ≥ 2t.

Citations

• Equilateral triangles in subsets of \Bbb R^d of large Hausdorff dimension

Related

• Long paths in the distance graph over large subsets of vector spaces over finite fields
• Generalized point configurations in \mathbb F_q^d
• Distance graphs in vector spaces over finite fields, coloring and pseudo-randomness
• Distance sets of two subsets of vector spaces over finite fields
• Interpolation of point configurations in the discrete plane