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11 votes
2 answers
425 views

Maximization of a cubic form over the $14$-dimensional sphere

For any integers $i$ and $j$ such as $1\le i<j\le6$, let $x_{ij}$ be a nonnegative real number. Is it true that, given the condition $$\sum_{1\le i<j\le6}x_{ij}^2=1,$$ the sum $$\sum_{1\le i<...
Iosif Pinelis's user avatar
2 votes
1 answer
754 views

On a combinatorial inequality

Is it true that \begin{gather} \min\left(\lambda_{\min}(M_{12}), \lambda_{\min}(M_{13}), \lambda_{\min}(M_{14}), \lambda_{\min}(M_{15}), \lambda_{\min}(M_{23}), \\ \lambda_{\min}(M_{24}), \lambda_{\...
Jasmine's user avatar
  • 178
11 votes
0 answers
291 views

$L_2$ minimizing makespan vs. $L_\infty$ minimizing makespan

There are $n$ positive real numbers. We partition these numbers into $m$ parts, the size of each part is the sum the numbers in this part. Maximum size of the parts is called a makespan of a partition....
kakia's user avatar
  • 399
14 votes
2 answers
963 views

Conjecture on maximum of symmetric combinatoric function

A curious symmetric function crossed my way in some quantum mechanics calculations, and I'm interested its maximum value (for which I do have a conjecture). (The question was first asked at math.SE, ...
Mario Krenn's user avatar