Image partition regularity near zero. (English) Zbl 1202.05146

De, Dibyendu; Hindman, Neil

Discrete Math. 309, No. 10, 3219-3232 (2009).

Summary: Many of the classical results of Ramsey Theory are naturally stated in terms of image partition regularity of matrices. Many characterizations are known of image partition regularity over \(\mathbb N\) and other subsemigroups of \((\mathbb R,+)\). We study several notions of image partition regularity near zero for both finite and infinite matrices, and establish relationships which must hold among these notions.

MSC:

05D10	Ramsey theory
05B20	Combinatorial aspects of matrices (incidence, Hadamard, etc.)

Keywords:

Ramsey theory; image partition regular matrix; central sets theorem

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