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Journal Articles Discrete Mathematics and Theoretical Computer Science Year : 2007

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.

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Dates and versions

hal-00579823 , version 1 (28-03-2011)
hal-00579823 , version 2 (03-06-2014)

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Olivier Bodini, Damien Jamet. Tiling a Pyramidal Polycube with Dominoes. Discrete Mathematics and Theoretical Computer Science, 2007, Vol. 9 no. 2 (2), pp.241-254. ⟨10.46298/dmtcs.413⟩. ⟨hal-00579823v1⟩
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