Perfect and Optimal Rulers

Generating and counting.

• What is a perfect ruler? A short introduction.
  In English, in German, in French and in Russian.
  
  
• The basic definitions: Rulers which are complete can have
  nice properties like being length-maximal or marker-minimal.
  A more formal description.
  
  
• Counting rulers: All checked values known.
  Here is a table, some samples and the perfect ruler pyramid
  and all optimal rulers with length <= 101.
  New: A list of all minimal prime number rulers.
  
  
• Generating rulers: Ruler hacking is hard!
  A coder's starter kit in C#, a Sage worksheet and a
  Maple worksheet. 'Rulez', a Java program for the fast
  generation of perfect and optimal rulers.
  'Kamm', an alternative program by Klaus Nagel in C,
  here adapted to Java. A Fortran program by
  Hugo Pfoertner for complete rulers.
   
• Wichmann rulers: A great idea to find big rulers.
  Here used for searching optimal rulers with length > 1000.
  A table and insights from a discussion on de.sci.mathematik.
  Are optimal rulers Wichmann rulers? A conjecture.
  
  
• Fun! How to craft a perfect ruler by hand.
  A Java applet by Klaus Nagel.
  
  
• References to the Online Encyclopedia of Integer Sequences, an overview.
  

Thanks to Hugo Pfoertner and Rainer Rosenthal for for many helpful and encouraging comments.

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Rational Trees	Orbitals	Eulerian Polynomials	vonStaudt Primes	Irregular Primes	Generalized Binomial
Bernoulli Confusion	Partitions Stirling	Zeta Polynomials	Perfect Rulers	Swinging Primes	Clausen Numbers
Hadamard Gamma	History Factorial	Permutation Trees	Swiss Knife	Swinging Factorial	Worpitzky Triangle