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Hegyvári Norbert: Variations on an intersection problem |
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| Raimi's theorem guarantees the existence of a partition of N into two parts with an unavoidable intersection property: for any finite coloring of N, some color class intersects both parts infinitely many times, after an appropriate shift (translation). We extend this result to higher dimension, in fact a stronger form that the translation will be "polynomial" shifts. We also prove some finite analogues of the above results for abelian groups and $SL_2(\mathbb{F}_q)$. This is a joint work with János Pach and Thang Pham. |
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