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The Number of Rooted Convex Polyhedra

Published online by Cambridge University Press:  20 November 2018

Edward A. Bender  and
Nicholas C. Wormald
Edward A. Bender
Affiliation:
Department of Mathematics, University of California at San Diego, La JollaCA 92093 USA
Nicholas C. Wormald
Affiliation:
Department of Mathematics and Statistics, The University of Auckland, Private Bag, Auckland, New Zealand
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Abstract

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Let pij be the number of rooted convex polyhedra with i + 1 vertices and j + 1 faces. We express pij as a singly indexed summation whose terms decrease geometrically. From this we deduce that

uniformly as max(i, j) → ∞.

Keywords

05C30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 31 , Issue 1 , 01 March 1988 , pp. 99 - 102
Copyright
Copyright © Canadian Mathematical Society 1988

References

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3. Mullin, R. C. and Schellenberg, P. J., The enumeration of c-nets via quadrangulations, J. Combin. Theory 3 (1968), pp. 259–276.Google Scholar
4. Tutte, W. T., A census of planar triangulations, Canad. J. Math. 15 (1963), pp. 249–271 Google Scholar