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Some Polyomino Tilings of the Plane

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arxiv math/9905012 v1 pith:GH3AK4T7 submitted 1999-05-03 math.CO

Cristopher Moore This is my paper · ORCID
classification math.CO
keywords tetrominotilingslowerplaneallowsboundboundscalculate
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Signed puzzles for Schubert coefficients

    math.CO 2025-04 conditional novelty 7.0 of 10

    A signed tiling rule computes every Schubert coefficient, and the rule implies a new polynomiality result for coefficient sums with bounded inversions.

  2. Automatic Enumeration of Tilings by Polyominoes

    math.CO 2026-07 conditional novelty 5.0 of 10

    Automated transfer-matrix enumeration yields rational generating functions for L-tetromino tilings of k×n boards for k=5,...,9, with several sequences not currently in the OEIS.

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