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general.hpp File Reference

General plans regarding investigations on Rado problems. More...

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Detailed Description

General plans regarding investigations on Rado problems.

The standard generalised Rado problems are given by Rado parameter lists [A_1, ..., A_m], where each A_i is a matrix of integers of dimension r_i x p_i, demanding a p_i-tuple x with A_i * x = 0.

The two main cases are the "full form" with m=1, and the "generalised form" where all r_i = 1. For these two cases it is known when the Ramsey-property holds and when not.

For the injective versions we demand the components of x to be different.

The numbers are called rado_m(A_1, ..., A_m) resp. radoi_m(A_1, ..., A_r).

Todo:
Connections
Todo:
Density versions
  • What is known about the independence numbers of the hypergraphs?

Definition in file general.hpp.