Coloring (number theory)

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Under a coloring is understood in the discrete number theory coloring a set of numbers with colors . The coloring of sets of numbers is mainly used in Ramsey theory , which examines under certain conditions to what extent regularities can be found in colored subsets.


Be different colors. The mapping defines a so-called coloration on a subset of the positive integers , through which each element of the subset is assigned one of the colors.


  • For each color from there is a tuple with . If this is not the case for one , we speak of a coloration.
  • If there is only one color for each .
  • The number of different stains can easily be obtained by some combinatorial effort.
  • With the above points it immediately follows that it has to be.
  • The coloring of the number is always arbitrary. For this reason, the concept of coloring is used in Ramsey theory , which tries to find out conditions for certain regularities for colored subsets.


We choose and . There are these numbers several colorations possible for would

1 2 3 4th 5 6th 7th
R. B. G B. R. R. G

While the definition of colors is used, concrete examples of these i. d. R. Colors such as red, green, blue are used.