Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds by Birkhoff Interpolation   In this paper we give lower bounds for the representation of real univariate
polynomials as sums of powers of degree 1 polynomials. We present two families
of polynomials of degree d such that the number of powers that are required in
such a representation must be at least of order d. This is clearly optimal up
to a constant factor. Previous lower bounds for this problem were only of order
$\Omega$($\sqrt$ d), and were obtained from arguments based on Wronskian
determinants and "shifted derivatives." We obtain this improvement thanks to a
new lower bound method based on Birkhoff interpolation (also known as "lacunary
polynomial interpolation").

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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga