Transitive factorisations into transpositions and holomorphic mappings on the sphere
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- by I. P. Goulden and D. M. Jackson PDF
- Proc. Amer. Math. Soc. 125 (1997), 51-60 Request permission
Abstract:
We determine the number of ordered factorisations of an arbitrary permutation on $n$ symbols into transpositions such that the factorisations have minimal length and such that the factors generate the full symmetric group on $n$ symbols. Such factorisations of the identity permutation have been considered by Crescimanno and Taylor in connection with a class of topologically distinct holomorphic maps on the sphere. As with Macdonald’s construction for symmetric functions that multiply as the classes of the class algebra, essential use is made of Lagrange inversion.References
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Additional Information
- I. P. Goulden
- Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- MR Author ID: 75735
- Email: ipgoulden@math.uwaterloo.ca
- D. M. Jackson
- Affiliation: Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
- MR Author ID: 92555
- Email: dmjackson@dragon.uwaterloo.ca
- Received by editor(s): July 20, 1995
- Communicated by: Jeffry N. Kahn
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 51-60
- MSC (1991): Primary 05A15; Secondary 05E99, 58C10, 70H20
- DOI: https://doi.org/10.1090/S0002-9939-97-03880-X
- MathSciNet review: 1396978