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- W2963378737 abstract "A matrix A is image partition regular over Q provided that whenever Q - {0} is finitely coloured, there is a vector x with entries in Q - {0} such that the entries of Ax are monochromatic. It is kernel partition regular over Q provided that whenever Q - {0} is finitely coloured, the matrix has a monochromatic member of its kernel. We establish a duality for these notions valid for both finite and infinite matrices. We also investigate the extent to which this duality holds for matrices partition regular over proper subsemigroups of Q." @default.
- W2963378737 created "2019-07-30" @default.
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- W2963378737 date "2017-01-01" @default.
- W2963378737 modified "2023-09-24" @default.
- W2963378737 title "Duality for image and kernel partition regularity of infinite matrices" @default.
- W2963378737 doi "https://doi.org/10.4310/joc.2017.v8.n4.a5" @default.
- W2963378737 hasPublicationYear "2017" @default.
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