We consider the problem of bounding the maximum possible number f<sub>k,d</sub>(n) of k-simplices that are spanned by a set of n pointsin R<sup>d</sup> and are similar to a given simplex. We firstâ€¦ (More)

We show that the number of unit-area triangles determined by a set of n points in the plane is O(n<sup>9/4+Îµ</sup>), for any Îµ>0, improving the recent bound O(n<sup>44/19</sup>) of Dumitrescu et al.

Given a set <i>P</i> of points in the plane we are interested in points that are 'deep' in the set in the sense that they have two opposite quadrants both containing many points of <i>P</i>. We dealâ€¦ (More)

Let I(n, l) denote the maximum possible number of incidences between n points and l lines. It is well known that I(n, l) = Î˜((nl) + n+ l) [2, 3, 7]. Let CSzTr denote the constant of proportionalityâ€¦ (More)

We show that if the number I of incidences between m points and n planes in R is sufficiently large, then the incidence graph (that connects points to their incident planes) contains a large completeâ€¦ (More)