Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Equivalence of M$^\natural$-concavity of a Set Function and
  Submodularity of Its Conjugate   A fundamental theorem in discrete convex analysis states that a set function
is M$^\natural$-concave if and only if its conjugate function is submodular.
This paper gives a new proof to this fact.

0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin