@article{9465,
  abstract     = {Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.},
  author       = {Edelsbrunner, Herbert and Nikitenko, Anton and Osang, Georg F},
  issn         = {14208997},
  journal      = {Journal of Geometry},
  number       = {1},
  publisher    = {Springer Nature},
  title        = {{A step in the Delaunay mosaic of order k}},
  doi          = {10.1007/s00022-021-00577-4},
  volume       = {112},
  year         = {2021},
}