Table of Clebsch–Gordan coefficients: Difference between revisions

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A '''perfect ruler''' of length <math>n</math> is a ruler with a [[subset]] of the [[integer]] markings <math>\{0,a_2,\cdots,a_n\}\subset\{0,1,2,\ldots,n\}</math> that appear on a regular ruler. The defining criterion of this subset is that there exists an <math>m</math> such that any [[positive integer]] <math>k\leq m</math> can be expressed uniquely as a [[Difference (mathematics)|difference]] <math>k=a_i-a_j</math> for some <math>i,j</math>. This is referred to as an <math>m</math>-perfect ruler.
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A 4-perfect ruler of length <math>7</math> is given by <math>\{0,1,3,7\}</math>. To verify this, we need to show that every number <math>1,2,3,4</math> can be expressed as a difference of two numbers in the above set:
 
: <math> 1=1-0</math>
 
: <math> 2=3-1</math>
 
: <math> 3=3-0</math>
 
: <math> 4=7-3</math>
 
An [[Optimization (mathematics)|optimal]] perfect ruler is one where for a fixed value of <math>n</math> the value of <math>a_n</math> is minimized.
 
 
==See also==
*[[Golomb ruler]]
 
*[[Sparse ruler]]
 
{{PlanetMath attribution|id=31620|title=perfect ruler}}
 
[[Category:Combinatorics]]

Latest revision as of 21:49, 17 November 2014

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