Milliken–Taylor theorem

Milliken–Taylor theorem This article may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (December 2014) (Learn how and when to remove this template message) In mathematics, the Milliken–Taylor theorem in combinatorics is a generalization of both Ramsey's theorem and Hindman's theorem. It is named after Keith Milliken and Alan D. Taylor.

Let {displaystyle {mathcal {P}}_{f}(mathbb {N} )} denote the set of finite subsets of {displaystyle mathbb {N} } , and define a partial order on {displaystyle {mathcal {P}}_{f}(mathbb {N} )} by α<β if and only if max α 0, let {displaystyle [FS(langle a_{n}rangle _{n=0}^{infty })]_{<}^{k}=left{left{sum _{tin alpha _{1}}a_{t},ldots ,sum _{tin alpha _{k}}a_{t}right}:alpha _{1},cdots ,alpha _{k}in {mathcal {P}}_{f}(mathbb {N} ){text{ and }}alpha _{1}

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