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Number of factors in K-cycle decompositions of permutations

Part of the Lecture Notes in Mathematics book series (LNM,volume 560)

Abstract

Let π be a permutation in Sn, the symmetric group on n letters. Let k be an integer, 2 ⩽ k ⩽ n, and suppose that π can be represented as a product of k-cycles. Denote by fk(π) the minimal number of k-cycles required for such a representation. In this paper bounds for fk(π) are derived. These bounds are used to determine \(\mathop {\lim }\limits_{n \to \infty }\) for all k, where fk(n)=max{fk(π) | π ε Sn}.

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References

  1. E. Bertram, Even permutations as a product of two conjugate cycles, J. Comb. Theory (A) 12 (1972), 368–380.

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  3. M. Herzog and K.B. Reid, Representation of permutations as products of cycles of fixed length, J. Austral. Math. Soc. (to appear).

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© 1976 Springer-Verlag

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Herzog, M., Reid, K.B. (1976). Number of factors in K-cycle decompositions of permutations. In: Casse, L.R.A., Wallis, W.D. (eds) Combinatorial Mathematics IV. Lecture Notes in Mathematics, vol 560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097373

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  • DOI: https://doi.org/10.1007/BFb0097373

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-08053-4

  • Online ISBN: 978-3-540-37537-1

  • eBook Packages: Springer Book Archive