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4 questions
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<...
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_{\...
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....
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, ...