A signed tiling rule computes every Schubert coefficient, and the rule implies a new polynomiality result for coefficient sums with bounded inversions.
Some Polyomino Tilings of the Plane
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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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Signed puzzles for Schubert coefficients
A signed tiling rule computes every Schubert coefficient, and the rule implies a new polynomiality result for coefficient sums with bounded inversions.