Polyomino convolutions and tiling problems

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Kisisel A.

JOURNAL OF COMBINATORIAL THEORY SERIES A, vol.95, no.2, pp.373-380, 2001 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 95 Issue: 2
  • Publication Date: 2001
  • Doi Number: 10.1006/jcta.2000.3171
  • Journal Name: JOURNAL OF COMBINATORIAL THEORY SERIES A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.373-380
  • Keywords: polyomino, tiling, coloring
  • Middle East Technical University Affiliated: Yes

Abstract

We define a convolution operation on the set of polyominoes and use it to obtain a criterion for a given polyomino not to tile the plane (rotations and translations allowed). We apply the criterion to several families of polyominoes and show that the criterion detects some cases that are not detectable by generalized coloring arguments. (C) 2001 Academic Press.