An improvement on the number of simplices in F-q(d)
Title: An improvement on the number of simplices in F-q(d) Authors: Pham Duc Hiep Pham Thang Le Anh Vinh Keywords: Finite fields Simplex Triangle Distinct distance subset Distances Issue Date: 2017 Publisher: ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS Citation: ISIKNOWLEDGE Abstract: Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Cartesian product of sets. Namely, we show that if kd epsilon is the Cartesian product of sets and [GRAHICS] = o(\epsilon\), the number of congruence classes of k-simplices determined by epsilon is at least (1 - omicron(1)) Description: TNS07078 ; DISCRETE APPLIED MATHEMATICS Volume: 221 Pages: 95-105 Published: APR 20 2017 URI: http://repository.vnu.edu.vn/handl...