Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear quantum addition rules   The quantum integer $[n]_q$ is the polynomial $1 + q + q^2 + ... + q^{n-1}.$
Two sequences of polynomials $\mathcal{U} = \{u_n(q)\}_{n=1}^{\infty}$ and
$\mathcal{V} = \{v_n(q)\}_{n=1}^{\infty}$ define a {\em linear addition rule}
$\oplus$ on a sequence $\mathcal{F} = \{f_n(q)\}_{n=1}^{\infty}$ by
$f_m(q)\oplus f_n(q) = u_n(q)f_m(q) + v_m(q)f_n(q).$ This is called a {\em
quantum addition rule} if $[m]_q \oplus [n]_q = [m+n]_q$ for all positive
integers $m$ and $n$. In this paper all linear quantum addition rules are
determined, and all solutions of the corresponding functional equations
$f_m(q)\oplus f_n(q) = f_{m+n}(q)$ are computed.

20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas