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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 1998; 35(1): 225-235

Printed March 1, 1998

Copyright © The Korean Mathematical Society.

Genus distributions for bouquets of dipoles

Jin Hwan Kim and Jaeun Lee

Yeungnam University and Yeungnam University

Abstract

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We compute genus distributions for bouquets of dipoles by using the method concerning the cycle structure of permutations in the symmetric group. From this, we can deduce that every bouquet of dipoles is upper embeddable. We find a formula for computing the embedding polynomials for bouquets of dipoles.

Keywords: bouquet of dipoles, $2$-cell embedding, rotation system, genus distribution, embedding polynomial

MSC numbers: 05C10

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