Károlyi Gyula: On subset sums of dense sets of integers

Abstract:

Let A be a set of n integers in the interval [1,k], where k<2n-5.
Denote by s(A) the sum of the elements in A. We prove that
if n is large enough, then every integer in the interval
[2k-2n+1,s(A)-2k+2n-1] can be represented as the sum of some
elements in A. This confirms an old conjecture of Lev.
Our proof depends on the Dias da Silva-Hamidoune theorem
and on an earlier result of Lev.

For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).