Editing Golomb ruler (section)

===Golomb rulers as sets===
A set of integers <math>A = \{a_1,a_2,...,a_m\}</math> where <math>a_1 < a_2 < ... < a_m</math> is a Golomb ruler if and only if

:<math>\text{for all } i,j,k,l \in \left\{1,2,...,m\right\} \text{such that } i \neq j \text{ and } k \neq l,\ a_i - a_j = a_k - a_l \iff i=k \text{ and } j=l.</math><ref>{{cite web
  | last = Dimitromanolakis
  | first = Apostolos
  | title = Analysis of the Golomb Ruler and the Sidon Set Problems, and Determination of Large, Near-Optimal Golomb Rulers
  | url = http://www.cs.toronto.edu/%7Eapostol/golomb/main.pdf
  | access-date = 2009-12-20
  }}</ref>

The ''order'' of such a Golomb ruler is <math>m</math> and its ''length'' is <math>a_m - a_1</math>. The [[canonical form]] has <math>a_1 = 0</math> and, if <math>m>2</math>, <math>a_2 - a_1 < a_m - a_{m-1}</math>. Such a form can be achieved through translation and reflection.