Omnimosaics

Details Omnimosaics Omnimosaics

2010-09-23

arxiv.org/abs/1009.4626v1

Mathematics

Combinatorics

19 pages

Scientific paper

An {\it omnimosaic} $O(n,k,a)$ is defined to be an $n\times n$ matrix, with entries from the set ${\cal A}=\{1,2,\...,a\}$, that contains, as a submatrix, each of the $a^{k^2}$ $k\times k$ matrices over ${\cal A}$. We provide constructions of omnimosaics and show that for fixed $a$ the smallest possible size $\omega(k,a)$ of an $O(n,k,a)$ omnimosaic satisfies \[\frac{ka^{k/2}}{e}\le \omega(k,a)\le \frac{ka^{k/2}}{e}(1+o(1))\] for a well-specified function $o(1)$ that tends to zero as $k\to\infty$.

Affiliated with

Also associated with

No associations

Rating

Omnimosaics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Omnimosaics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Omnimosaics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-339030