@article{58,
  abstract     = {Inside a two-dimensional region (``cake""), there are m nonoverlapping tiles of a certain kind (``toppings""). We want to expand the toppings while keeping them nonoverlapping, and possibly add some blank pieces of the same ``certain kind,"" such that the entire cake is covered. How many blanks must we add? We study this question in several cases: (1) The cake and toppings are general polygons. (2) The cake and toppings are convex figures. (3) The cake and toppings are axis-parallel rectangles. (4) The cake is an axis-parallel rectilinear polygon and the toppings are axis-parallel rectangles. In all four cases, we provide tight bounds on the number of blanks.},
  author       = {Akopyan, Arseniy and Segal Halevi, Erel},
  journal      = {SIAM Journal on Discrete Mathematics},
  number       = {3},
  pages        = {2242 -- 2257},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Counting blanks in polygonal arrangements}},
  doi          = {10.1137/16M110407X},
  volume       = {32},
  year         = {2018},
}