Omnimosaics

الأصل · EN

An omnimosaic O(n,k,a) is defined to be an n× n matrix, with entries from the set A={1,2,..,a}, that contains, as a submatrix, each of the aᵏ² k× k matrices over A. We provide constructions of omnimosaics and show that for fixed a the smallest possible size ω(k,a) of an O(n,k,a) omnimosaic satisfies kaᵏ/²e≤ ω(k,a)≤ kaᵏ/²e(1+o(1)) for a well-specified function o(1) that tends to zero as k→∞.