The Coin Exchange Problem and the Structure of Cube Tilings

Details The Coin Exchange Problem and the Structure of Cube Tilings The Coin Exchange Problem and the Structure of Cube Tilings

2008-07-06

arxiv.org/abs/0807.0891v1

Mathematics

Combinatorics

3 pages

Scientific paper

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.

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