Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering Equations: Real Solutions and Particles on a Line   We find $n(n-3)/2$-dimensional regions of the space of kinematic invariants,
where all the solutions to the scattering equations (the core of the CHY
formulation of amplitudes) for $n$ massless particles are real. On these
regions, the scattering equations are equivalent to the problem of finding
stationary points of $n-3$ mutually repelling particles on a finite real
interval with appropriate boundary conditions. This identification directly
implies that for each of the $(n-3)!$ possible orderings of the $n-3$ particles
on the interval, there exists one stable stationary point. Furthermore,
restricting to four dimensions, we find that the separation of the solutions
into $k\in \{2,3,\ldots ,n-2\}$ sectors naturally matches that of permutations
of $n-3$ labels into those with $k-2$ descents. This leads to a physical
realization of the combinatorial meaning of the Eulerian numbers.

6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas