skip to main content
article
Free Access

Loopless Algorithms for Generating Permutations, Combinations, and Other Combinatorial Configurations

Authors Info & Claims
Published:01 July 1973Publication History
Skip Abstract Section

Abstract

The purpose of this work is to find a method for building loopless algorithms for listing combinatorial items, like partitions, permutations, combinations. Gray code, etc. Algorithms for the above sequence are detailed in full.

References

  1. 1 JOHNSON, S.M. Generat,on of permutations by adjacent transpositions. Math. Comput. 17 (1963), 282-285.Google ScholarGoogle Scholar
  2. 2 TROTTER, H.F. Algorithm 115, Perm Comm. A CM 5, 8 (Aug. 1962), 434-435. Google ScholarGoogle Scholar
  3. 3 EVEN, S. Algorithmic Combinatomcs Macmillan, New York, 1973, p. 2.Google ScholarGoogle Scholar
  4. 4 EHRLm~, G. Four combinatoriM algorithms: PERMU. Permutations (to appear in Comm. A CM). COMBI: Combinations (to appear in Comm ACM). COMPOMIN: Compositions with minima (to appear in Comm. ACM). COMPOMAX: Compositions with maxima (to appear in Comm. A CM). See als~ PARTI' Part,t,ons of a set (m manuscript). GRAY2: Reflected binary Gray code (in manuscript).Google ScholarGoogle Scholar
  5. 5 ~,~D-S~ITH, R.J. Generation of permutation sequences: Part 2. Compuler J. 14 (May 1971), 136-139.Google ScholarGoogle Scholar
  6. 6 BOOTHROID, j. Algorithm 30. Computer J. 10 (1967), 310Google ScholarGoogle Scholar
  7. 7 GILBERT, E N Gray codes and paths on the n-cube. Bell Syst. Tech J 37 (May 1958), 815-826.Google ScholarGoogle Scholar
  8. 8 CHASE, P J. Algorithm 382, Combmatmns of M out of N objects. Comm. ACM lS, 6 (June 1970), 368 See also Remark on Algorithm 382, p. 376. Google ScholarGoogle Scholar
  9. 9 EHRLICH, G. PATEXACT: Generator of set-partitions to exactly R subsets (to appear).Google ScholarGoogle Scholar

Index Terms

  1. Loopless Algorithms for Generating Permutations, Combinations, and Other Combinatorial Configurations

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image Journal of the ACM
        Journal of the ACM  Volume 20, Issue 3
        July 1973
        175 pages
        ISSN:0004-5411
        EISSN:1557-735X
        DOI:10.1145/321765
        Issue’s Table of Contents

        Copyright © 1973 ACM

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 July 1973
        Published in jacm Volume 20, Issue 3

        Permissions

        Request permissions about this article.

        Request Permissions

        Check for updates

        Qualifiers

        • article

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader