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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

Monomials as sums of powers: The real binary case


Authors: Mats Boij, Enrico Carlini and Anthony V. Geramita
Journal: Proc. Amer. Math. Soc. 139 (2011), 3039-3043
MSC (2010): Primary 14P99; Secondary 13A02, 15A21
Published electronically: April 25, 2011
MathSciNet review: 2811260
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Abstract | References | Similar Articles | Additional Information

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.


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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
Email: Anthony.Geramita@gmail.com, geramita@dima.unige.it

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11018-9
Received by editor(s): May 17, 2010
Published electronically: April 25, 2011
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society