Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Application of multivariate splines to discrete mathematics   Using methods developed in multivariate splines, we present an explicit
formula for discrete truncated powers, which are defined as the number of
non-negative integer solutions of linear Diophantine equations. We further use
the formula to study some classical problems in discrete mathematics as
follows. First, we extend the partition function of integers in number theory.
Second, we exploit the relation between the relative volume of convex polytopes
and multivariate truncated powers and give a simple proof for the volume
formula for the Pitman-Stanley polytope. Third, an explicit formula for the
Ehrhart quasi-polynomial is presented.

1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an