Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On double Hurwitz numbers with completed cycles   In this paper, we collect a number of facts about double Hurwitz numbers,
where the simple branch points are replaced by their more general analogues ---
completed (r+1)-cycles. In particular, we give a geometric interpretation of
these generalised Hurwitz numbers and derive a cut-and-join operator for
completed (r+1)-cycles. We also prove a strong piecewise polynomiality property
in the sense of Goulden-Jackson-Vakil. In addition, we propose a conjectural
ELSV/GJV-type formula, that is, an expression in terms of some intrinsic
combinatorial constants that might be related to the intersection theory of
some analogues of the moduli space of curves. The structure of these
conjectural "intersection numbers" is discussed in detail.

18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph