perfect ruler

A perfect rulerMathworldPlanetmath of length n is a ruler with a subset of the integer markings {0,a2,,n}{0,1,2,,n} that appear on a regular ruler. The defining criterion of this subset is that there exists an m such that any positive integer km can be expresses uniquely as a difference k=ai-aj for some i,j. This is referred to as an m-perfect ruler.

A 4-perfect ruler of length 7 is given by {0,1,3,7}. To verify this, we need to show that every number 1,2,,4 can be expressed as a difference of two numbers in the above set:

1 =1-0
2 =3-1
3 =3-0
4 =7-3

An optimal perfect ruler is one where for a fixed value of n the value of an is minimized.

Title perfect ruler
Canonical name PerfectRuler
Date of creation 2013-03-22 12:14:22
Last modified on 2013-03-22 12:14:22
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 12
Author mathcam (2727)
Entry type Definition
Classification msc 03E02
Classification msc 05A17
Synonym Golomb ruler