3 × 3永久物的警戒等级

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2020-07-01 DOI:10.1137/20m1349254

Y. Shitov

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引用次数: 4

摘要

设f是一个d次齐次多项式，其系数在域f中满足char f = 0或char f > d。f的Waring秩是最小的整数r，使得f是f -线性形式的r次方的线性组合。证明了多项式x1 y2 z3 + x1 y3 z2 + x2 y1 z3 + x2 y3 z1 + x3 y1 z2 + x3 y2 z1的Waring秩至少为16，符合已知的上界。

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The Waring Rank of the 3 x 3 Permanent

Let f be a homogeneous polynomial of degree d with coefficients in a field F satisfying char F = 0 or char F > d. The Waring rank of f is the smallest integer r such that f is a linear combination of r powers of F-linear forms. We show that the Waring rank of the polynomial x1 y2 z3 + x1 y3 z2 + x2 y1 z3 + x2 y3 z1 + x3 y1 z2 + x3 y2 z1 is at least 16, which matches the known upper bound.

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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量