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- W4214904865 abstract "We show the existence of several infinite monochromatic patterns in the integers obtained as values of suitable symmetric polynomials; in particular, we obtain extensions of both the additive and multiplicative versions of Hindman's theorem. These configurations are obtained by means of suitable symmetric polynomials that mix the two operations. The simplest example is the following. For every finite coloring N=C1∪…∪Cr there exists an infinite increasing sequence a<b<c<… such that all elements below are monochromatic:a,b,c,…,a+b+ab,a+c+ac,b+c+bc,…,a+b+c+ab+ac+bc+abc,…. The proofs use tools from algebra in the space of ultrafilters βZ." @default.
- W4214904865 created "2022-03-05" @default.
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- W4214904865 date "2022-07-01" @default.
- W4214904865 modified "2023-09-26" @default.
- W4214904865 title "Infinite monochromatic patterns in the integers" @default.
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- W4214904865 doi "https://doi.org/10.1016/j.jcta.2022.105610" @default.
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