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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Cycle decompositions and train tracks


Authors: Charles A. Matthews and David J. Wright
Journal: Proc. Amer. Math. Soc. 132 (2004), 3411-3415
MSC (2000): Primary 57N99, 20B30, 32G15, 30F99
Published electronically: June 16, 2004
MathSciNet review: 2073318
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that the disjoint cycle decomposition of the permutation $(1 \, 2 \cdots n_1)^{k_1} (1 \, 2 \cdots n_2)^{k_2} \cdots (1 \, 2 \cdots n_r)^{k_r}$ consists of cycles of at most $r$ distinct lengths. The proof relies on the geometry and topology of simple closed curves and train tracks on a closed surface of genus $r$.


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Additional Information

Charles A. Matthews
Affiliation: Department of Mathematics, Southeastern Oklahoma State University, Durant, Oklahoma 74701
Email: cmatthews@sosu.edu

David J. Wright
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74075
Email: wrightd@math.okstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07515-X
PII: S 0002-9939(04)07515-X
Keywords: Cycle decomposition, train track, multiple curve
Received by editor(s): February 18, 2002
Received by editor(s) in revised form: November 10, 2002
Published electronically: June 16, 2004
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society