17 citations · 23 across the 5 of their papers we have counts for
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math.CO2012
A Pseudoline Counterexample to the Strong Dirac Conjecture
Ben D. Lund, George B. Purdy, Justin W. Smith
We demonstrate an infinite family of pseudoline arrangements, in which an arrangement of n pseudolines has no member incident to more than 4n/9 points of intersection. This shows t…
math.CO2010★ 3 cited
A Bichromatic Incidence Bound and an Application
Ben D. Lund, George B. Purdy, Justin W. Smith
We prove a new, tight upper bound on the number of incidences between points and hyperplanes in Euclidean d-space. Given n points, of which k are colored red, there are O_d(m^{2/3}…
math.CO2009★ 3 cited
Lines, Circles, Planes and Spheres
George B. Purdy, Justin W. Smith
Let be a set of points in , no three collinear and not all coplanar. If at most are coplanar and is sufficiently large, the total number of planes d…