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Tiling a Pyramidal Polycube with Dominoes

Abstract : The notion of pyramidal polycubes, namely the piling-up of bricks of a non-increasing size, generalizes in R^n the concept of trapezoidal polyominoes. In the present paper, we prove that n-dimensional dominoes can tile a pyramidal polycube if and only if the latter is balanced, that is, if the number of white cubes is equal to the number of black ones for a chessboard-like coloration, generalizing the result of [BC92] when n=2.
Keywords : polyomino tiling domino
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  • HAL Id : hal-00579823, version 2

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Olivier Bodini, Damien Jamet. Tiling a Pyramidal Polycube with Dominoes. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, 9 (2), pp.241-254. ⟨hal-00579823v2⟩

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