A generalization of a result of Sylvester's |
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Authors: | MJ Knight |
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Institution: | Department of Mathematics, The University of Texas at El Paso, El Paso, Texas 79968 USA |
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Abstract: | Let v1,…,vn be vectors in Zn with D = det(v1,…,vn) > 0. Let vn + 1 be in the cone generated by v1,…,vn and such that v1,…,vv, vn + 1 generate Zn as a Z-module. There exists a unique “largest“ χ not expressible as a nonnegative integer combination of v1,…,vn, vn + 1 and χ = Dvn + 1 ? (v1 + … vn + vn + 1). |
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