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On the Enumeration of Rooted Non-Separable Planar Maps

Published online by Cambridge University Press:  20 November 2018

W. G. Brown  and
W. T. Tutte
W. G. Brown
Affiliation:
University of British Columbia and University of Waterloo
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It has been shown elsewhere (1, 4) that the number of rooted non-separable planar maps with n edges is

In the present paper we improve upon this result by finding the number fi,j of rooted non-separable planar maps with i + 1 vertices and j + 1 faces. We use the definitions of (1).

Among the non-separable planar maps only the loop-map and the link-map have i = 0 or j = 0. We therefore confine our attention to the case in which i and j are both positive.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 572 - 577
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Brown, W. G., Enumeration of non-separable planar maps, Can. J. Math., 15 (1963), 526– 545.Google Scholar
2. Good, I. J., Generalizations to several variables of Lagrange's expansion, with applications to stochastic processes, Proc. Camb. Phil. Soc, 56 (1960), 367–380.Google Scholar
3. Goursat, E., A course in mathematical analysis, I and II, Part I (Boston, 1904 and 1916).Google Scholar
4. Tutte, W. T., A census of planar maps, Can. J. Math., 15 (1963), 249–271.Google Scholar