Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A tour of the Weak and Strong Lefschetz Properties   An artinian graded algebra, $A$, is said to have the Weak Lefschetz property
(WLP) if multiplication by a general linear form has maximal rank in every
degree. A vast quantity of work has been done studying and applying this
property, touching on numerous and diverse areas of algebraic geometry,
commutative algebra, and combinatorics. Amazingly, though, much of this work
has a "common ancestor" in a theorem originally due to Stanley, although
subsequently reproved by others. In this expository paper we describe the
different directions in which research has moved starting with this theorem,
and we discuss some of the open questions that continue to motivate current
research.

8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg