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.
Highlights
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O ÅÓÓÖ Ò ÂoÅo ÊÓ ×ÓÒo ÀÖØÐÒ ÔÖÓ Ð Ñ× Û Ø × ÑÔÐ Ø Ð ×o ×1 Ö Ø 2 ÓÑÔÙØ Ø ÓÒ Ð ÓÑ ØÖÝ 3⁄4 ́ μ ¿ 1⁄4 ̧ 3⁄41⁄41⁄41⁄2o
Summary
To cite this version: Olivier Bodini, Damien Jamet. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, 9 (2), pp.241254. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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