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- W4300777941 abstract "Let $G$ be a finite abelian group with exponent $n$, and let $r$ be a positive integer. Let $A$ be a $ktimes m$ matrix with integer entries. We show that if $A$ satisfies some natural conditions and $|G|$ is large enough then, for each $r$--coloring of $Gsetminus {0}$, there is $delta$ depending only on $r,n$ and $m$ such that the homogeneous linear system $Ax=0$ has at least $delta |G|^{m-k}$ monochromatic solutions. Density versions of this counting result are also addressed." @default.
- W4300777941 created "2022-10-04" @default.
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- W4300777941 date "2012-03-11" @default.
- W4300777941 modified "2023-09-27" @default.
- W4300777941 title "On the number of monochromatic solutions of integer linear systems on Abelian groups" @default.
- W4300777941 doi "https://doi.org/10.48550/arxiv.1203.2383" @default.
- W4300777941 hasPublicationYear "2012" @default.
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