On the Ramsey number of the Brauer configuration
| Autor: | Jonathan Chapman, Sean Prendiville |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Mathematics - Number Theory General Mathematics 010102 general mathematics Double exponential function Inverse 01 natural sciences Exponential function Quadratic equation FOS: Mathematics Mathematics - Combinatorics Van der Waerden's theorem 11B30 05D10 Combinatorics (math.CO) Number Theory (math.NT) Ramsey's theorem 0101 mathematics Mathematics |
| Zdroj: | Bulletin of the London Mathematical Society. 52:316-334 |
| ISSN: | 1469-2120 0024-6093 |
| DOI: | 10.1112/blms.12327 |
| Popis: | We obtain a double exponential bound in Brauer's generalisation of van der Waerden's theorem, which concerns progressions with the same colour as their common difference. Such a result has been obtained independently and in much greater generality by Sanders. Using Gowers' local inverse theorem, our bound is quintuple exponential in the length of the progression. We refine this bound in the colour aspect for three‐term progressions, and combine our arguments with an insight of Lefmann to obtain analogous bounds for the Ramsey numbers of certain non‐linear quadratic equations. |
| Databáze: | OpenAIRE |
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