Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Totally real algebraic integers of arboreal height 2   In arXiv:1302.4423, Salez proved that every totally real algebraic integer is
the eigenvalue of some tree. We define the "arboreal height" of a totally real
algebraic integer $\lambda$ to be the minimal height of a rooted tree having
$\lambda$ as an eigenvalue. In this paper, we prove several results about
totally real algebraic integers of arboreal height $2$: We show that all real
quadratic integers have arboreal height $\le 2$. We characterize the totally
real cubic integers of arboreal height $2$. Finally, we prove that every
totally irrational real number field is generated (as a ring over $\mathbb{Q}$)
by some $\lambda$ of arboreal height $2$.

1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol