Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On distribution of the depth index on perfect matchings   We study the restriction of depth index statistic on the set of perfect
matchings. In particular, we provide additional combinatorial description of
the statistic for perfect matchings and calculate the generating polynomial.
The main result of the present short paper is that the depth index on perfect
matchings is equidistributed with the rank function of the Bruhat order.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con