Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong shellability of simplicial complexes   Imposing a strong condition on the linear order of shellable complexes, we
introduce strong shellability. Basic properties, including the existence of
dimension-decreasing strong shelling orders, are developed with respect to
nonpure strongly shellable complexes. Meanwhile, pure strongly shellable
complexes can be characterized by the corresponding codimension one graphs. In
addition, we show that the facet ideals of pure strongly shellable complexes
have linear quotients.

19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs