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Abstract: . Let T be a finite set of tiles. The group of invariants G(T), introduced by the author [P], 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. Introduction The problem of tileability of a region is very old, and in many instances computationally hard, even for small sets of tiles (see e.g. [MR,Ro]). The subject... (Update)
Active bibliography (related documents): More All
1.1: Ribbon Tile Invariants from Signed Area - Moore, Pak (2000) (Correct)
0.9: Tiling groups for Wang tiles - Moore, Rapaport, Rémila (Correct)
0.9: On Tilings By Ribbon Tetrominoes - Muchnik, Pak (1999) (Correct)
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0.3: Generalized Tilings with Height Functions - Bodini, Latapy (2001) (Correct)
0.2: Automatic Generation of Invariants in Processor Verification - Su, Dill, Barrett (1996) (Correct)
0.2: On Fine's Partition Theorems, Dyson, Andrews and Missed.. - Pak (2002) (Correct)
BibTeX entry: (Update)
@misc{ pak-tile,
author = "Igor Pak",
title = "Tile Invariants: New Horizons",
url = "citeseer.ist.psu.edu/pak00tile.html" }
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Documents on the same site (http://www-math.mit.edu/~pak/research.html): More
On Mixing Of Certain Random Walks, Cutoff Phenomenon And Sharp.. - Pak, Vu (1999) (Correct)
On the Number of Faces of Certain Transportation Polytopes - Pak (2000) (Correct)
Reduced decompositions of permutations in terms of star.. - Pak (1999) (Correct)
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