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On the number of nonorientable Wicks forms in a free group

Published online by Cambridge University Press:  14 November 2011

A. Vdovina
A. Vdovina
Affiliation:
Higher Algebra Chair, Mechanical-Mathematics Department, Moscow State University, Moscow, 117234, Russian Federation
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Abstract

The paper is concerned with the estimation of the number of maximal-length genus n nonorientable Wicks forms for n → ∞. It is shown how to apply a graph theory for this problem. It is proved that if M(n) be the number of all nonequivalent nonorientable genus n Wicks forms of maximal length, then

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 1 , 1996 , pp. 113 - 116
Copyright
Copyright © Royal Society of Edinburgh 1996

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References

1Bender, E. A. and Caunfield, E. R.. The asymptotic number of labeled graphs with given degree sequences. J. Combin. Theory Ser. A 24 (1978), 296–307.CrossRefGoogle Scholar
2Comerford, L. P., Comerford, J. A. and Edmunds, C. C.. Powers as products of commutators. Comm. Algebra 19(1991), 675–84.Google Scholar
3Culler, M.. Using surfaces to solve equations in free groups. Topology 20 (1981), 133–45.CrossRefGoogle Scholar
4OPshanskii, A.Homomorphism diagrams of surface groups. Siberian Math. J. 30 (1989), 961–79.Google Scholar
5Read, R. C.. Some unusual enumeration problems. Ann. New York Acad. Sci. 175 (1970), 314–26.Google Scholar
6Vdovina, A.. Products of squares in a free group. Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. 1(1994), 26–30.Google Scholar
7Wicks, M. J.. The equation x2y2 = g over free products. Proc. Cong. Sing. Nat. Acad. of Sci. (1971), 238–48.Google Scholar