2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164319Let 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 pagesCombinatoricsNumber Theory05A18, 52C22, 05B45, 11H99text