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Enumeration of Non-Separable Planar Maps

Published online by Cambridge University Press:  20 November 2018

William G. Brown
William G. Brown*
Affiliation:
University of Toronto
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In (2), Tutte has shown that the number, Bn, of rooted non-separable planar maps having n edges is [2(3n — 3)!]/[n! (2n — 1)!]. Rooting was accomplished by designating one edge as the root, orienting it, and distinguishing between its sides as left and right. We shall here compute the number, Bn,m, of rooted non-separable planar maps having n edges and such that the face to the left of the root is incident with exactly m edges, which maps will be said to be of type [n, m].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 526 - 545
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. Tutte, W. T., A census of planar triangulations, Can. J. Math., 14 (1962), 21–38.Google Scholar
2. Tutte, W. T., A census of planar maps, Can. J. Math. 15 (1963), 249–271.Google Scholar
3. Vinogradov, I. M., Elements of number theory (New York, 1954).Google Scholar
4. Whittaker, E. T. and Watson, G. N., A course of modern analysis (Cambridge, 1927).Google Scholar