Orientations of chain groups |
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Authors: | Oliver Pretzel |
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Affiliation: | (1) Mathematics Department, Imperial College, SW7 London, U.K. |
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Abstract: | We prove generalizations to chain groups, of Minty's Arc Colouring Lemma and its extension, the well-known Farkas Lemma. In these the orientation of the edges is replaced by an arbitrary chain.A function on a chain groupN isrepresentable if there exists a chainR such that (X)=R·X for allXN. Anorientation is a chain with values ±1. We prove that for a regular chain group a linear function that is representable by an orientation for each chainXN locally, is representable by an orientation globally. |
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Keywords: | 05B35 90C27 05C38 |
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