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Mathematicians can now explain how many people would need to be invited to a party so at least 4 people always know one another. It only took 90 years to solve.
A 2-colouring of K 5 with no monochromatic K 3. The conclusion to the theorem does not hold if we replace the party of six people by a party of less than six. To show this, we give a coloring of K 5 with red and blue that does not contain a triangle with all edges the same color. We draw K 5 as a pentagon surrounding a star (a pentagram). We ...
The Ramsey problem, or Ramsey pricing, or Ramsey–Boiteux pricing, is a second-best policy problem concerning what prices a public monopoly should charge for the various products it sells in order to maximize social welfare (the sum of producer and consumer surplus) while earning enough revenue to cover its fixed costs.
Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of the mathematical field of combinatorics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask a question of the form: "how big must some structure be to guarantee ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
The problem is closely linked to the problem of socially optimal monopolistic pricing when profits are constrained to be positive, known as the Ramsey problem. He was the first to make a significant contribution to the theory of optimal taxation from an economic standpoint, and much of the literature that has followed reflects Ramsey's initial ...
Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory.Van der Waerden's theorem states that for any given positive integers r and k, there is some number N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, then there are at least k integers in arithmetic progression whose elements are of the same color.
The mistake is in the book p. 872! Ruleof3 10:46, 11 March 2007 (UTC) Perhaps this reference should be added to the article. —Steztric 11:52, 5 November 2010 (UTC) Does this really apply to "monopolists" only, as stated in the first sentence?? —Preceding unsigned comment added by 24.167.147.246 03:30, 2 September 2008 (UTC)