Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric functions and the principal case of the Frankl-F\"uredi
  conjecture   Let $r\geq3$ and $G$ be an $r$-uniform hypergraph with vertex set $\left\{
1,\ldots,n\right\} $ and edge set $E$. Let \[ \mu\left( G\right) :=\max
{\textstyle\sum\limits_{\left\{ i_{1},\ldots,i_{r}\right\} \in E}}
x_{i_{1}}\cdots x_{i_{r}}, \] where the maximum is taken over all nonnegative
$x_{1},\ldots,x_{n}$ with $x_{1}+\cdots+x_{n}=1.$
  Let $t\geq r-1$ be the unique real number such that $\left\vert E\right\vert
=\binom{t}{r}$. It is shown that if $r\leq5$ or $t\geq4\left( r-1\right) \left(
r-2\right) $, then \[ \mu\left( G\right) \leq t^{-r}\binom{t}{r}% \] with
equality holding if and only if $t$ is an integer.
  The proof is based on some new bounds on elementary symmetric functions.

25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph