Discrete Mathematics & Theoretical Computer Science, Vol 9, No 2 (2007)

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Tiling a Pyramidal Polycube with Dominoes

Olivier Bodini, Damien Jamet


The notion of pyramidal polycubes, namely the piling-up of bricks of a non-increasing size, generalizes in ℝn 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

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