Progressions in Sequences of Nearly Consecutive Integers

Abstract

For k > 2 and r ≥ 2, letG(k, r) denote the smallest positive integer g such that every increasing sequence of g integers {a1, a2, . . . , ag} with gaps aj+1 − aj ∈ {1, . . . , r}, 1 ≤ j ≤ g − 1 contains a k-term arithmetic progression. Brown and Hare [4] proved that G(k, 2) > √ (k − 1)/2( 43 ) (k−1)/2 and that G(k, 2s−1) > (sk−2/ek)(1+o(1)) for all s ≥ 2… (More)
DOI: 10.1006/jcta.1998.2886

Topics

Cite this paper

@article{Alon1998ProgressionsIS, title={Progressions in Sequences of Nearly Consecutive Integers}, author={Noga Alon and Ayal Zaks}, journal={J. Comb. Theory, Ser. A}, year={1998}, volume={84}, pages={99-109} }