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Results tagged with inequalities
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user 13639
for questions involving inequalities, upper and lower bounds.
2
votes
1
answer
138
views
Lower Bound for $\sum_{\{i,j\}\subseteq \partial S \\ (g_i-g_j)^2 \le1}{(g_i-g_j)^2}$
Let $\emptyset \subsetneq S \subsetneq \{1,\cdots,n\}$ be a set with cardinality $s$, and $g\in\mathbb{R}^n$ be a vector such that
$$\sum_{\{i,j\}\subseteq \{1,\cdots,n\}}{(g_i-g_j)^2} = s(n-s).$$
…
- 519
13
votes
2
answers
792
views
Distance of vectors versus distance of their difference vectors
For any given $x \in \mathbb{R}^n$, let $\nabla{x} \in \mathbb{R}^{n \choose 2}$ be the vector whose $\{i,j\}$-th entry is $|x_i-x_j|$. I think the following claim is true.
Claim. If $f, g \in \m …
- 519