David Eppstein - Publications

Publications with Takashi Horiyama

• Multifold tiles of polyominoes and convex lattice polygons.
  K. Chida, E. Demaine, M. Demaine, D. Eppstein, A. Hesterberg, T. Horiyama, J. Iacono, H. Ito, S. Langerman, R. Uehara, and Y. Uno.
  23rd Thailand-Japan Conference on Discrete and Computational Geometry, Graphs, and Games, 2021, pp. 28–29.
  Thai Journal of Mathematics 21 (4): 957–978, 2023.

  We investigate shapes whose congruent copies can cover the plane exactly \(k\) times per point, but not a number of times that is a nonzero integer smaller than \(k\). We find polyominoes with this property for all \(k\ge 2\), and convex integer-coordinate polygons with this property for \(k=5\) and for all \(k\ge 7\).