Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Why the characteristic polynomial factors   We survey three methods for proving that the characteristic polynomial of a
finite lattice factors over the nonnegative integers and indicate how they have
evolved recently. The first technique uses geometric ideas and is based on
Zaslavsky's theory of signed graphs. The second approach is algebraic and
employs results of Saito and Terao about free hyperplane arrangements. Finally,
we consider a purely combinatorial theorem of Stanley about semimodular
supersolvable lattices and its generalizations.

22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th