(In reply to
kudos by Ady TZIDON)
Is this right?
1. A Golomb Ruler has 2 properties:
a. Order (number of marks, including 0)
b. length (maximum mark)
2. A Justin Ruler (or Tzidon Set) has 3 properties:
a. order (j)
b. length (l)
c. range (R). The range is the sum of the last 2 marks
3. For a given order, the formula 1/2n(n+1)+2 gives the theoretical minimum range for a Justin Ruler of that order. This range is the 'canonical range', Rc
4. A ruler is a Justin Ruler if
a. the sum of every pair of marks is distinct from that of every other pair.
b. the range of the ruler is a minimum for a ruler of that order.
5. A Justin Ruler is perfect if its range is Rc for a ruler of that order
6. If the range, Rj of a Justin Ruler of a particular order exceeds Rc, then the difference is the looseness (RjRc) or the fractional looseness (1 (Rc/Rj))*100%) of the Ruler
7. For obvious reasons, the minimum order of a Justin Ruler is 4
Edited on July 21, 2010, 7:00 am

Posted by broll
on 20100721 06:58:37 