Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the lengths of zigzags in thin complexes   We consider zigzags in thin complexes. The main result states that the sum of
the lengths of all zigzags in an $n$-complexe is equal to the sum of the
lengths of all zigzags in all $(n-1)$-faces of this complex, and this sum also
is the twice of the sum of the lengths of all zigzags in all $(n-2)$-faces. For
simplicial and cubical $n$-complexes, the sum depends on the rank $n$ and the
number of $(n-1)$-faces only. We also describe the sum of the lengths of all
generalized zigzags, it depends on the rank and the number of flags. As an
application, we find the number of zigzags in Coxeter complexes.

7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex