Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balanced complexes and complexes without large missing faces   The face numbers of simplicial complexes without missing faces of dimension
larger than $i$ are studied. It is shown that among all such
$(d-1)$-dimensional complexes with non-vanishing top homology, a certain
polytopal sphere has the componentwise minimal $f$-vector; and moreover, among
all such 2-Cohen--Macaulay (2-CM) complexes, the same sphere has the
componentwise minimal $h$-vector. It is also verified that the $l$-skeleton of
a flag $(d-1)$-dimensional 2-CM complex is $2(d-l)$-CM while the $l$-skeleton
of a flag PL $(d-1)$-sphere is $2(d-l)$-homotopy CM. In addition, tight lower
bounds on the face numbers of 2-CM balanced complexes in terms of their
dimension and the number of vertices are established.

13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat