Tile invariants: new horizons

Authors:
Igor Pak
Affiliations:
Department of Mathematics, MIT, Cambridge, MA
Venue:
Theoretical Computer Science - Special issue: Tilings of the plane
Year:
2003

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Abstract

Let T be a finite set of tiles. The group of invariants G(T), introduced by Pak (Trans. AMS 352 (2000) 5525), is a group of linear relations between the number of copies of tiles in tilings of the same region. We survey known results about G, the height function approach, the local move property, various applications and special cases.