Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $\gamma$-vector of a barycentric subdivision   We prove that the $\gamma$-vector of the barycentric subdivision of a
simplicial sphere is the $f$-vector of a balanced simplicial complex. The
combinatorial basis for this work is the study of certain refinements of
Eulerian numbers used by Brenti and Welker to describe the $h$-vector of the
barycentric subdivision of a boolean complex.

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys