Generation of permutations following Lehmer and Howell

Author:
Enrico Spoletini

Journal:
Math. Comp. **43** (1984), 565-572

MSC:
Primary 05A05

DOI:
https://doi.org/10.1090/S0025-5718-1984-0758204-3

MathSciNet review:
758204

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper proves two formulas used to obtain, by an arithmetic method, both the next permutation with respect to a given one and the *m*th permutation, in lexicographic direct ordering.

**[1]**J. R. Howell, "Generation of permutations by addition,"*Math. Comp.*, v. 16, 1962, pp. 243-244. MR**0144828 (26:2369)****[2]**J. R. Howell, "Algorithm 87: Permutation generator,"*Comm. ACM*, v. 5, 1962, p. 209.**[3]**D. H. Lehmer,*Teaching Combinatorial Tricks to a Computer*, Proc. Sympos. Appl. Math. Combinatorial Analysis, Vol. 10, Amer. Math. Soc., Providence, R. I., 1960, pp. 179-193. MR**0113289 (22:4127)****[4]**E. S. Page & L. B. Wilson,*An Introduction to Computational Combinatorics*, Cambridge Univ. Press, 1979. MR**561109 (81d:68001)****[5]**R. Sedgewick, "Permutation generation methods,"*Comput. Surveys*, v. 9, 1977, pp. 137-163. MR**0464682 (57:4607)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1984-0758204-3

Keywords:
Permutations,
lexicographic ordering,
lexicographic generation,
permutation generation

Article copyright:
© Copyright 1984
American Mathematical Society