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Representation of permutations as products of cycles of fixed length

Published online by Cambridge University Press:  09 April 2009

Marcel Herzog  and
K. B. Reid
Marcel Herzog
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT 2600.Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel.
K. B. Reid
Affiliation:
Department of Mathematics, Institute of Advanced Studies, The Australian National University, Canberra, ACT 2600. Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A. Department of Mathematics, Tel-Aviv University, Tel-Aviv, Israel..
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Abstract

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We study the problem of representing a permutation C as a product of a minimum number, fk(C), of cycles of length k. Upper and lower bounds on fk(C) are obtained and exact results are derived for k = 2, 3, 4.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 3 , November 1976 , pp. 321 - 331
Copyright
Copyright © Australian Mathematical Society 1976

References

Feit, W., Lyndon, R., and Scott, L. (1975), ‘A remark about permutations’, J. Combinatorial Theory 18, 234–235.Google Scholar
Ree, R. (1971), ‘A theorem on permutations’, J. Combinatorial Theory 10, 174–175.CrossRefGoogle Scholar