They define Π(n) as the number of unit squares that can cover a square of side length n+ϵ. It appears that the status as of this 2008 paper was that Π(n)=n2+O(n2/3) has been established, and they conjecture that Π(n)=n2+Ω(n1/2).
Jun 25, 2010
Covering a square of side n+ε with unit squares - ScienceDirect
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Here I pose an analogous problem for squares and show that in order to cover a square of side length, unit squares suffice.
(Sketchy) proof, using e instead of epsilon: To cover the square of side length n+e : Place n by n unit squares as a square of side length n in the lower left ...
Here I pose an analogous problem for squares and show that in order to cover a square of side length n + ε, n2 + o(1)n + O(1) unit squares suffice. This problem ...
Our main question is to find the smallest number of unit squares that can cover a square of side length n+ε, where n is a positive integer and ε is a ...
This chapter discusses the development of Prime Number Theory from Euclid to Hardy and Littlewood to current state-of-the-art, published in Springer ...
Here I pose an analogous problem for squares and show that in order to cover a square of side length n + ε , n 2 + o 1 n + O 1 unit squares suffice. This ...
Given a set P of n points in R2, we consider two related problems. Firstly, we study the problem of computing two isothetic unit squares which may be either ...
We consider the dual problem of finding the side s(n) of the largest square that can be covered with n unit squares. From area considerations, it is trivial ...
Oct 11, 2005 · To cover it with unit squares we will use a square grid in the lower left (n − k) × (n − k) subsquare, and 1 × (k + 1) polyominos in covering ...