Monomials as sums of powers: The real binary case
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- by Mats Boij, Enrico Carlini and Anthony V. Geramita PDF
- Proc. Amer. Math. Soc. 139 (2011), 3039-3043 Request permission
Abstract:
We generalize an example, due to Sylvester, and prove that any monomial of degree $d$ in $\mathbb {R}[x_0, x_1]$, which is not a power of a variable, cannot be written as a linear combination of fewer than $d$ powers of linear forms.References
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Additional Information
- Mats Boij
- Affiliation: Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden
- Email: boij@kth.se
- Enrico Carlini
- Affiliation: Dipartimento di Matematica, Politecnico di Torino, 10129 Turin, Italy
- Email: enrico.carlini@polito.it
- Anthony V. Geramita
- Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada, K7L 3N6 – and – Dipartimento di Matematica, Università di Genova, 16126 Genoa, Italy
- MR Author ID: 72575
- Email: Anthony.Geramita@gmail.com, geramita@dima.unige.it
- Received by editor(s): May 17, 2010
- Published electronically: April 25, 2011
- Communicated by: Irena Peeva
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 3039-3043
- MSC (2010): Primary 14P99; Secondary 13A02, 15A21
- DOI: https://doi.org/10.1090/S0002-9939-2011-11018-9
- MathSciNet review: 2811260