Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper and lower bounds on the size of $B_k[g]$ sets   A subset $A$ of the integers is a $B_k[g]$ set if the number of multisets
from $A$ that sum to any fixed integer is at most $g$. Let $F_{k,g}(n)$ denote
the maximum size of a $B_k[g]$ set in $\{1,\dots, n\}$. In this paper we
improve the best-known upper bounds on $F_{k,g}(n)$ for $g>1$ and $k$ large.
When $g=1$ we match the best upper bound of Green with an improved error term.
Additionally, we give a lower bound on $F_{k,g}(n)$ that matches a construction
of Lindstr\"om while removing one of the hypotheses.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas