Common Unfoldings of Polyominoes and Polycubes

نویسندگان

  • Greg Aloupis
  • Prosenjit Bose
  • Sébastien Collette
  • Erik D. Demaine
  • Martin L. Demaine
  • Karim Douïeb
  • Vida Dujmovic
  • John Iacono
  • Stefan Langerman
  • Pat Morin
چکیده

Abstract. This paper studies common unfoldings of various classes of polycubes, as well as a new type of unfolding of polyominoes. Previously, Knuth and Miller found a common unfolding of all tree-like tetracubes. By contrast, we show here that all 23 tree-like pentacubes have no such common unfolding, although 22 of them have a common unfolding. On the positive side, we show that there is an unfolding common to all “non-spiraling” k-ominoes, a result that extends to planar non-spiraling k-cubes.

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تاریخ انتشار 2010