The number of monochromatic Schur triples (Q1970081)
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scientific article; zbMATH DE number 1417662
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The number of monochromatic Schur triples |
scientific article; zbMATH DE number 1417662 |
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The number of monochromatic Schur triples (English)
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27 September 2000
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Solving a problem of Graham, Rödl and Ruciński, it is shown that in every 2-coloring of the set \(\{1,\ldots,N\}\) one can find at least \(N^2/22 + O(N)\) monochromatic Schur triples, i.e.~monochromatic solutions of the equation \(x+y=z\). Moreover, based on this result the exact value of the infimum number of Schur triples in any 2-coloring of \(\{1,\ldots,N\}\) can be found.
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Schur triple
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Ramsey theory
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