Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T01:24:59.317Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bender, E. A. and Richmond, L. B., 77*e asymptotic enumeration of rooted convex polyhedra, J. Combin. Theory Ser. B. 36 (1984), pp. 276–283.Google Scholar
2. Bender, E. A. and Wormald, N. C., Almost all convex polyhedra are asymmetric, Canad. J. Math. 27 (1985), pp. 854–871.Google Scholar
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