ENCORE: An $\mathcal{O}(N_{\rm g}^2)$ Estimator for Galaxy $N$-Point
  Correlation Functions
  We present a new algorithm for efficiently computing the $N$-point
correlation functions (NPCFs) of a 3D density field for arbitrary $N$. This can
be applied both to a discrete spectroscopic galaxy survey and a continuous
field. By expanding the statistics in a separable basis of isotropic functions
built from spherical harmonics, the NPCFs can be estimated by counting pairs of
particles in space, leading to an algorithm with complexity $\mathcal{O}(N_{\rm
g}^2)$ for $N_{\rm g}$ particles, or $\mathcal{O}\left(N_\mathrm{FFT}\log
N_\mathrm{FFT}\right)$ when using a Fast Fourier Transform with
$N_\mathrm{FFT}$ grid-points. In practice, the rate-limiting step for $N>3$
will often be the summation of the histogrammed spherical harmonic
coefficients, particularly if the number of radial and angular bins is large.
In this case, the algorithm scales linearly with $N_{\rm g}$. The approach is
implemented in the ENCORE code, which can compute the 3PCF, 4PCF, 5PCF, and
6PCF of a BOSS-like galaxy survey in $\sim$ $100$ CPU-hours, including the
corrections necessary for non-uniform survey geometries. We discuss the
implementation in depth, along with its GPU acceleration, and provide practical
demonstration on realistic galaxy catalogs. Our approach can be
straightforwardly applied to current and future datasets to unlock the
potential of constraining cosmology from the higher-point functions.
