Distribution of pinned distance trees in the plane Fp2

Authors

• Steven Senger, Missouri State UniversityFollow
• Thang Pham, Vietnam National University, Hanoi
• The Dung Tran, Vietnam National University, Hanoi

Abstract

The recent result of Guth, Iosevich, Ou, and Wang (2019) on the Falconer distance problem states that for a compact set A?R², if the Hausdorff dimension of A is greater than [Formula presented], then the distance set ?(A) has positive Lebesgue measure. With a completely different approach, Murphy, Petridis, Pham, Rudnev, and Stevens (2022) proved the prime field version of this result, namely, for E?Fp² with |E|?p^5/4, there exist many points x?E such that the number of distinct distances from x is at least cp. The main purpose of this paper is to prove extensions in the more general structure of pinned trees. The case of distances on small sets will also be addressed in this paper.

Department(s)

Mathematics

Document Type

Article

DOI

10.1016/j.disc.2023.113613

Keywords

Configurations, Dense sets, Distances, Finite fields

Publication Date

12-1-2023

Recommended Citation

Senger, Steven; Pham, Thang; and Tran, The Dung, "Distribution of pinned distance trees in the plane Fp2" (2023). Faculty Scholarship. 521.
https://bearworks.missouristate.edu/articles00/521

Journal Title

Discrete Mathematics