Generation of permutations following Lehmer and Howell

Author:
Enrico Spoletini

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

MSC:
Primary 05A05

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]**John R. Howell,*Generation of permutations by addition*, Math. Comp.**16**(1962), 243–244. MR**0144828**, 10.1090/S0025-5718-1962-0144828-9**[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., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 179–193. MR**0113289****[4]**E. S. Page and L. B. Wilson,*An introduction to computational combinatorics*, Cambridge Computer Science Texts, vol. 9, Cambridge University Press, New York, 1979. MR**561109****[5]**Robert Sedgewick,*Permutation generation methods*, Comput. Surveys**9**(1977), no. 2, 137–164. MR**0464682**

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Additional Information

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

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

Article copyright:
© Copyright 1984
American Mathematical Society