Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4949698 | Discrete Applied Mathematics | 2017 | 11 Pages |
Abstract
Let E be a set of points in Fqd. Bennett et al. (2016) proved that if |E|â«qdâdâ1k+1 then E determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when E is the Cartesian product of sets. Namely, we show that if E is the Cartesian product of sets and qkdk+1â1âd=o(|E|), the number of congruence classes of k-simplices determined by E is at least (1âo(1))qk+12, and in some cases our result is sharp.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Duc Hiep Pham, Thang Pham, Le Anh Vinh,