Small sets which meet all the k(n)-term arithmetic progressions in the interval [1, n]

Abstract

For given r-z, k, the minimum cardinal of any subset B of [l, n] which meets all of the k-term arithmetic progressions contained in Cl, n] is denoted by f(n, k). We show, answering questions raised by Professor P. Erdiis, that f(n, ne) < C . n’-’ for some constant C (where C depends on E), and that f(n, log n) = o(n). We also discuss the behavior of f(p2, p) when p is a prime, and we give a simple lower bound for the function associated with Szemeredi’s theorem.

DOI: 10.1016/0097-3165(89)90049-6

Cite this paper

@article{Brown1989SmallSW, title={Small sets which meet all the k(n)-term arithmetic progressions in the interval [1, n]}, author={Tom C. Brown and Allen R. Freedman}, journal={J. Comb. Theory, Ser. A}, year={1989}, volume={51}, pages={244-249} }