Gray codes, loopless algorithm and partitions

Toufik Mansour, Ghalib Nassar

Research output: Contribution to journalArticlepeer-review


The generation of efficient Gray codes and combinatorial algorithms that list all the members of a combinatorial object has received a lot of attention in the last few years. Knuth gave a code for the set of all partitions of [n] = {1,2,...,n}. Ruskey presented a modified version of Knuth's algorithm with distance 2. Ehrlich introduced a looplees algorithm for the set of the partitions of [n]; Ruskey and Savage generalized Ehrlich's results and introduced two Gray codes for the set of partitions of [n]. In this paper, we give another combinatorial Gray code for the set of the partitions of [n] which differs from the aforementioned Gray codes. Also, we construct a different loopless algorithm for generating the set of all partitions of [n] which gives a constant time between successive partitions in the construction process.

Original languageEnglish
Pages (from-to)291-310
Number of pages20
JournalJournal of Mathematical Modelling and Algorithms
Issue number3
StatePublished - Sep 2008


  • Gray codes
  • Loopless algorithms
  • Partitions
  • Plane trees

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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