A Construction for Partitions Which Avoid Long Arithmetic Progressions

Author:

Berlekamp E.R.

Abstract

For k ≥2, t ≥2, let W(k, t) denote the least integer m such that in every partition of m consecutive integers into k sets, atleast one set contains an arithmetic progression of t+1 terms. This paper presents a construction which improves the best previously known lower bounds on W(k, t) for small k and large t.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

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