Transitive factorisations into transpositions and holomorphic mappings on the sphere
Authors:
I. P. Goulden and D. M. Jackson
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
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Abstract | References | Similar Articles | Additional Information
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 Macdonaldâs construction for symmetric functions that multiply as the classes of the class algebra, essential use is made of Lagrange inversion.
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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
Article copyright:
© Copyright 1997
American Mathematical Society
