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{\bf Yan Yang and Yanpei Liu}
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{\bf Classification of ($p,q,n$)-Dipoles on Nonorientable Surfaces}
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A type of rooted map called $(p,q,n)$-dipole, whose numbers on
surfaces have some applications in string theory, are defined and
the numbers of $(p,q,n)$-dipoles on orientable surfaces of genus 1
and 2 are given by Visentin and Wieler (The Electronic Journal of
Combinatorics 14 (2007),\#R12). In this paper, we study the
classification of $(p,q,n)$-dipoles on nonorientable surfaces and
obtain the numbers of $(p,q,n)$-dipoles on the projective plane
and Klein bottle.



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