Article ID Journal Published Year Pages File Type
4949698 Discrete Applied Mathematics 2017 11 Pages PDF
Abstract
Let E be a set of points in Fqd. Bennett et al. (2016) proved that if |E|≫qd−d−1k+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+1−1∕d=o(|E|), the number of congruence classes of k-simplices determined by E is at least (1−o(1))qk+12, and in some cases our result is sharp.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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