The Coin Exchange Problem and the Structure of Cube Tilings

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Let k_1,...,k_d be positive integers, and D be a subset of [k_1]x...x[k_d], whose complement can be decomposed into disjoint sets of the form {x_1}x...x{x_{s-1}}x[k_s]x{x_{s+1}}x...x{x_d}. We conjecture that the number of elements of D can be represented as a linear combination of the numbers k_1,..., k_d with non-negative integer coefficients. A connexion of this conjecture with the structure of periodical cube tilings is revealed.
3 pages

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Combinatorics, Number Theory, 05A18, 52C22, 05B45, 11H99

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http://salesiana.dossiersoluciones.com/handle/123456789/164319

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.0891
 http://arxiv.org/abs/0807.0891

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arXiv