Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Real-rootedness of Eulerian Polynomials via the Hermite--Biehler
  Theorem   Based on the Hermite--Biehler theorem, we simultaneously prove the
real-rootedness of Eulerian polynomials of type $D$ and the real-rootedness of
affine Eulerian polynomials of type $B$, which were first obtained by Savage
and Visontai by using the theory of $\mathbf{s}$-Eulerian polynomials. We also
confirm Hyatt's conjectures on the interlacing property of half Eulerian
polynomials. Borcea and Br\"and\'en's work on the characterization of linear
operators preserving Hurwitz stability is critical to this approach.

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The categories of this paper are: hep-lat
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
18
The categories of this paper are: econ