An asymptotic bound on the composition number of integer sums of squares formulas

P. Hrubes; A. Wigderson; A. Yehudayoff

doi:10.4153/CMB-2011-143-x

An asymptotic bound on the composition number of integer sums of squares formulas

P. Hrubes^*
, A. Wigderson
, A. Yehudayoff

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let Z(k) be the smallest n such that there exists an identity (x ² + x²₂ + . . . + x²_k ).(y²₁ + y²₂ + . . . + y ²_k ) = f²₁ + f² ₂ + . . . + f²_n , with f₁, . . . , f_n being polynomials with integer coefficients in the variables x₁, . . . , x_k and y₁, . . . , y_k. We prove that Z(k) ≥(k^6/5).

Original language	English
Pages (from-to)	70-79
Number of pages	10
Journal	Canadian Mathematical Bulletin
Volume	56
Issue number	1
DOIs	https://doi.org/10.4153/CMB-2011-143-x
State	Published - 2013
Externally published	Yes

Keywords

Composition formulas
Radon-Hurwitz number
Sums of squares

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abstract = "Let Z(k) be the smallest n such that there exists an identity (x 2 + x22 + . . . + x2k ).(y21 + y22 + . . . + y 2k ) = f21 + f2 2 + . . . + f2n , with f1, . . . , fn being polynomials with integer coefficients in the variables x1, . . . , xk and y1, . . . , yk. We prove that Z(k) ≥(k6/5).",

keywords = "Composition formulas, Radon-Hurwitz number, Sums of squares",

author = "P. Hrubes and A. Wigderson and A. Yehudayoff",

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doi = "10.4153/CMB-2011-143-x",

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AU - Yehudayoff, A.

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N2 - Let Z(k) be the smallest n such that there exists an identity (x 2 + x22 + . . . + x2k ).(y21 + y22 + . . . + y 2k ) = f21 + f2 2 + . . . + f2n , with f1, . . . , fn being polynomials with integer coefficients in the variables x1, . . . , xk and y1, . . . , yk. We prove that Z(k) ≥(k6/5).

AB - Let Z(k) be the smallest n such that there exists an identity (x 2 + x22 + . . . + x2k ).(y21 + y22 + . . . + y 2k ) = f21 + f2 2 + . . . + f2n , with f1, . . . , fn being polynomials with integer coefficients in the variables x1, . . . , xk and y1, . . . , yk. We prove that Z(k) ≥(k6/5).

KW - Composition formulas

KW - Radon-Hurwitz number

KW - Sums of squares

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An asymptotic bound on the composition number of integer sums of squares formulas

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Keywords

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