Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: (k+1)-sums versus k-sums   A $k$-sum of a set $A\subseteq \mathbb{Z}$ is an integer that may be
expressed as a sum of $k$ distinct elements of $A$. How large can the ratio of
the number of $(k+1)$-sums to the number of $k$-sums be? Writing $k\wedge A$
for the set of $k$-sums of $A$ we prove that \[ \frac{|(k+1)\wedge A|}{|k\wedge
A|}\, \le \, \frac{|A|-k}{k+1} \] whenever $|A|\ge (k^{2}+7k)/2$. The
inequality is tight -- the above ratio being attained when $A$ is a geometric
progression. This answers a question of Ruzsa.

11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys