Invariant equations defining coincident root loci |
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Authors: | Email author" target="_blank">Jaydeep?V?ChipalkattiEmail author |
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Institution: | (1) Department of Mathematics, University of British Columbia, Vancouver, B.C., V6T 1Z2, Canada;(2) Present address: Department of Mathematics, University of Manitoba, 342 Machray Hall, Winnipeg, MB, R3T 2N2, Canada |
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Abstract: | Let F(x) = xn+1 xn-1+2 xn-2+ ··· +n be a polynomial with complex coefficients, and suppose we are given a partition (1,...,r) of n. It is a classical problem to determine explicit algebraic conditions on the i so that F may have roots with multiplicities 1,...,r. We give an invariant theoretic solution to this problem, to wit, we exhibit a set of covariants of F whose vanishing is a necessary and sufficient condition. The construction of such covariants is combinatorial, and involves associating a set of graphs on n vertices (called decisive graphs) to each .Received: 28 September 2003 |
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Keywords: | 12D10 13A50 14Q99 |
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