Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hurwitz numbers for real polynomials   We consider the problem of defining and computing real analogs of polynomial
Hurwitz numbers, in other words, the problem of counting properly normalized
real polynomials with fixed ramification profiles over real branch points. We
show that, provided the polynomials are counted with an appropriate sign, their
number does not depend on the order of the branch points on the real line. We
study generating series for the invariants thus obtained, determine necessary
and sufficient conditions for the vanishing and nonvanishing of these
generating series, and obtain a logarithmic asymptotic for the invariants as
the degree of the polynomials tends to infinity.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th