. C O ] 4 F eb 2 01 6 LARGE SUBSETS OF DISCRETE HYPERSURFACES IN Z d CONTAIN ARBITRARILY MANY COLLINEAR POINTS
نویسندگان
چکیده
Ramsey theory deals with the problem of finding structured configurations in suitably large but possibly disordered sets. The nature of the desired configurations can range from complete subgraphs of a graph to arithmetic progressions in Z to solutions of equations, such as x+y = z, in a countable commutative semigroup. In this paper we deal with configurations consisting of finitely many collinear points in Z. The following theorem, which deals with this type of configurations, was obtained by L. T. Ramsey in 1977:
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