61 citations · 249 across the 42 of their papers we have counts for
4 papers · 1 filter
Sums of dilates
Boris Bukh
The lambda-dilate of a set A is lambda*A={lambda a : a \in A}. We give an asymptotically sharp lower bound on the size of sumsets of the form lambda_1*A+...+lambda_k*A for arbitrar…
Discrete Kakeya-type problems and small bases
Noga Alon, Boris Bukh, Benny Sudakov
A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and…
Measurable sets with excluded distances
Boris Bukh
For a set of distances D={d_1,...,d_k} a set A is called D-avoiding if no pair of points of A is at distance d_i for some i. We show that the density of A is exponentially small in…
Non-trivial solutions to a linear equation in integers
Boris Bukh
For k>=3 let A \subset [1,N] be a set not containing a solution to a_1 x_1+...+a_k x_k=a_1 x_{k+1}+...+a_k x_{2k} in distinct integers. We prove that there is an epsilon>0 dependin…