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Abstract: We calculate the generating functions for the number of tilings of rectangles of various widths by the right tromino, the L tetromino, and the T tetromino. This allows us to place lower bounds on the entropy of tilings of the plane by each of these. For the T tetromino, we also derive a lower bound from the solution of the Ising model in two dimensions. (Update)
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BibTeX entry: (Update)
@misc{ moore-some,
author = "Cristopher Moore",
title = "Some Polyomino Tilings of the Plane",
url = "citeseer.ist.psu.edu/303374.html" }
Citations (may not include all citations):146 Computers and Intractibility: A Guide to the Theory of NP-Co.. (context) - Garey, Johnson - 1979
58 The undecidability of the domino problem (context) - Berger - 1966
48 The number of dimer arrangements on a quadratic lattice (context) - Kasteleyn, of et al. - 1961
47 Undecidability and nonperiodicity of tilings of the plane (context) - Robinson - 1971
12 Princeton University Press (context) - Golomb, Puzzles et al. - 1994
11 The Theory of Critical Phenomena: An Introduction to the Ren.. (context) - Binney, Dowrick et al. - 1992
2 Triangular trimers on the triangular lattice: an exact solut.. (context) - Verberkmoes, Nienhuis
1 Manuscript available at http://www-math (context) - Propp, dominoes
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