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- Rado's_theorem_(Ramsey_theory) abstract "Rado's theorem is a theorem from the branch of mathematics known as Ramsey theory. It is named for the German mathematician Richard Rado. It was proved in his thesis, Studien zur Kombinatorik.Let Ax = 0 be a system of linear equations, where A is a matrix with integer entries. This system is said to be r-regular if, for every r-coloring of the natural numbers 1, 2, 3, ..., the system has a monochromatic solution. A system is regular if it is r-regular for all r ≥ 1.Rado's theorem states that a system Ax=0 is regular if and only if the matrix A satisfies the columns condition. Let ci denote the i-th column of A. The matrix A satisfies the columns condition provided that there exists a partition C1, C2, ..., Cn of the column indices such that if , then s1 = 0 for all i ≥ 2, si can be written as a rational linear combination of the cj's in the Ck with k < i.Folkman's theorem, the statement that there exist arbitrarily large sets of integers all of whose nonempty sums are monochromatic, may be seen as a special case of Rado's theorem concerning the regularity of the system of equationswhere T ranges over each nonempty subset of the set {1, 2, ..., x}.".
- Rado's_theorem_(Ramsey_theory) wikiPageID "1706360".
- Rado's_theorem_(Ramsey_theory) wikiPageRevisionID "545346251".
- Rado's_theorem_(Ramsey_theory) hasPhotoCollection Rado's_theorem_(Ramsey_theory).
- Rado's_theorem_(Ramsey_theory) subject Category:Ramsey_theory.
- Rado's_theorem_(Ramsey_theory) subject Category:Theorems_in_discrete_mathematics.
- Rado's_theorem_(Ramsey_theory) type Abstraction100002137.
- Rado's_theorem_(Ramsey_theory) type Communication100033020.
- Rado's_theorem_(Ramsey_theory) type Message106598915.
- Rado's_theorem_(Ramsey_theory) type Proposition106750804.
- Rado's_theorem_(Ramsey_theory) type Statement106722453.
- Rado's_theorem_(Ramsey_theory) type Theorem106752293.
- Rado's_theorem_(Ramsey_theory) type TheoremsInDiscreteMathematics.
- Rado's_theorem_(Ramsey_theory) comment "Rado's theorem is a theorem from the branch of mathematics known as Ramsey theory. It is named for the German mathematician Richard Rado. It was proved in his thesis, Studien zur Kombinatorik.Let Ax = 0 be a system of linear equations, where A is a matrix with integer entries. This system is said to be r-regular if, for every r-coloring of the natural numbers 1, 2, 3, ..., the system has a monochromatic solution.".
- Rado's_theorem_(Ramsey_theory) label "Rado's theorem (Ramsey theory)".
- Rado's_theorem_(Ramsey_theory) label "Théorème de Rado (théorie de Ramsey)".
- Rado's_theorem_(Ramsey_theory) sameAs Théorème_de_Rado_(théorie_de_Ramsey).
- Rado's_theorem_(Ramsey_theory) sameAs m.05pyjw.
- Rado's_theorem_(Ramsey_theory) sameAs Q3527146.
- Rado's_theorem_(Ramsey_theory) sameAs Q3527146.
- Rado's_theorem_(Ramsey_theory) sameAs Rado's_theorem_(Ramsey_theory).
- Rado's_theorem_(Ramsey_theory) wasDerivedFrom Rado's_theorem_(Ramsey_theory)?oldid=545346251.
- Rado's_theorem_(Ramsey_theory) isPrimaryTopicOf Rado's_theorem_(Ramsey_theory).