Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inverse Problems for Representation Functions in Additive Number Theory   For every positive integer h, the representation function of order h
associated to a subset A of the integers or, more generally, of any group or
semigroup X, counts the number of ways an element of X can be written as the
sum (or product, if X is nonabelian) of h not necessarily distinct elements of
X. The direct problem for representation functions in additive number theory
begins with a subset A of X and seeks to understand its representation
functions. The inverse problem for representation functions starts with a
function f:X ->N_0 U {\infty} and asks if there is a set A whose representation
function is f, and, if the answer is yes, to classify all such sets. This paper
is a survey of recent progress on the inverse representation problem.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an