@article{5678,
abstract = {The order-k Voronoi tessellation of a locally finite set đť‘‹âŠ†â„ťđť‘› decomposes â„ťđť‘› into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold.},
author = {Edelsbrunner, Herbert and Nikitenko, Anton},
issn = {14320444},
journal = {Discrete and Computational Geometry},
number = {4},
pages = {865â€“878},
publisher = {Springer},
title = {{Poissonâ€“Delaunay Mosaics of Order k}},
doi = {10.1007/s00454-018-0049-2},
volume = {62},
year = {2019},
}