48 citations · 110 across the 37 of their papers we have counts for
5 papers · 1 filter
The joints problem for matroids
Larry Guth, Andrew Suk
We prove that in a simple matroid, the maximal number of joints that can be formed by L lines is o(L^2) and Omega(L^{2 - epsilon}) for any epsilon > 0.
New bounds on the maximum number of edges in -quasi-planar graphs
Andrew Suk, Bartosz Walczak
A topological graph is -quasi-planar if it does not contain pairwise crossing edges. A 20-year-old conjecture asserts that for every fixed , the maximum number of edges i…
A note on order-type homogeneous point sets
Andrew Suk
Let OT_d(n) be the smallest integer N such that every N-element point sequence in R^d in general position contains an order-type homogeneous subset of size n, where a set is order-…
A Ramsey-type result for geometric l-hypergraphs
Dhruv Mubayi, Andrew Suk
Let n \geq l \geq 2 and q \geq 2. We consider the minimum N such that whenever we have N points in the plane in general position and the l-subsets of these points are colored with…
Ramsey-type results for semi-algebraic relations
David Conlon, Jacob Fox, János Pach +2
A k-ary semi-algebraic relation E on R^d is a subset of R^{kd}, the set of k-tuples of points in R^d, which is determined by a finite number of polynomial equations and inequalitie…