2
votes
1answer
71 views

Range of inner product of a sequence and its permutation

$a^n :=(a_i)_1^n$ is a finite sequence of real numbers of length $n$, where $\sum\limits_{i=1}^n a_i=0$ and $\sum\limits_{i=1}^n a_i^2=1$. Consider $s_n(a^n,\sigma):=\sum\limits_{i=1}^n ...
0
votes
0answers
74 views

Can we find a function satisfiying the following functional inequation?

Question: I would be interested know if there exist (and construct) a function $f:\mathbb N\times \mathbb N \to (0,\infty )$ such that for all integers $p,q$, $f(p,q)=f(q,p)$ and a constant ...
0
votes
2answers
85 views

Counting $2010^2$-tuples

Here's a problem i invented myself, but i'm not sure about my solution. I'll show it later, so people can enjoy trying to find one: Consider the function $f:\mathbb{R}^2\to\{1,2,...,2012\}$ that ...