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/handle/VNU_123/29796
ISSN:	0166-218X
Appears in Collections:	Bài báo của ĐHQGHN trong Web of Science