Ribbon tile invariants from the signed area

Authors:
Cristopher Moore;Igor Pak
Affiliations:
Department of Computer Science and Department of Physics and Astronomy, University of New Mexico, Albuquerque, New Mexico;Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts
Venue:
Journal of Combinatorial Theory Series A
Year:
2002

Citing 7
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Abstract

Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were first introduced by the second author (2000, Trans. Amer. Math. Soc. 352, 5525-5561), where a full basis of invariants of ribbon tiles was conjectured. Here we present a complete proof of the conjecture, which works by associating ribbon tiles with certain polygons in the complex plane, and deriving invariants from the signed area of these polygons.