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On acyclic simplicial complexes

Published online by Cambridge University Press:  26 February 2010

Frank Harary  and
Edgar M. Palmer
Frank Harary
Affiliation:
University of Michigan
Edgar M. Palmer
Affiliation:
University College, London
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Extract

The higher dimensional concepts corresponding to trees are developed and studied. In order to enumerate these 2-dimensional structures called 2-trees, a dissimilarity characteristic theory is investigated. By an appropriate application of certain combinatorial techniques, generating functions are obtained for the number of 2-trees. These are specialized to count those 2-trees embeddable in the plane, thus providing a new approach to the old problem of determining the number of triangulations of a polygon.

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Type
Research Article
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Mathematika , Volume 15 , Issue 1 , June 1968 , pp. 115 - 122
Copyright
Copyright © University College London 1968

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