2002/10/31 by Mihail N. Kolountzakis, Kolountzakis, Mihail N. · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.math/0210476
6 pages, 2 figures
arxiv created 2002/10/31 · arxiv updated 2009/11/30
Suppose that A is a finite set of integers of diameter D. Suppose also that the set of integers B is such that A+B is a tiling of the integers, that is each integer is uniquely expressible as a+b, with a in A, b in B. It is well known that B must be a periodic set in this case. Here we study the relationship between the diameter D of A and the least period T of B. We show that T is at most C exp(C √ D log D √(loglog D)) and that we can have T at least quadratic in D.