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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Counting cycles in permutations by group characters, with an application to a topological problem


Author: D. M. Jackson
Journal: Trans. Amer. Math. Soc. 299 (1987), 785-801
MSC: Primary 05A15; Secondary 05A05, 20C30, 57N37
MathSciNet review: 869231
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Abstract: The character theory of the symmetric group is used to derive properties of the number of permutations, with $ k$ cycles, which are expressible as the product of a full cycle with an element of an arbitrary, but fixed, conjugacy class. For the conjugacy class of fixed point free involutions, this problem has application to the analysis of singularities in surfaces.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0869231-9
Article copyright: © Copyright 1987 American Mathematical Society