Abstract
We reconsider the classical problem of representing a finite number of forms of degree d in the polynomial ring over n + 1 variables as scalar combinations of powers of linear forms. We define a geometric construct called a ‘grove’, which, in a number of cases, allows us to determine the dimension of the space of forms which can be so represented for a fixed number of summands. We also present two new examples, where this dimension turns out to be less than what a naïve parameter count would predict.
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Carlini, E., Chipalkatti, J.V. On Waring’s problem for several algebraic forms . Comment. Math. Helv. 78, 494–517 (2003). https://doi.org/10.1007/s00014-003-0769-6
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DOI: https://doi.org/10.1007/s00014-003-0769-6