Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subdivision and spline spaces   A standard construction in approximation theory is mesh refinement. For a
simplicial or polyhedral mesh D in R^k, we study the subdivision D' obtained by
subdividing a maximal cell of D. We give sufficient conditions for the module
of splines on D' to split as the direct sum of splines on D and splines on the
subdivided cell. As a consequence, we obtain dimension formulas and explicit
bases for several commonly used subdivisions and their multivariate
generalizations.

17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga