Asymptotic Enumeration of Combinatorial Structures.
Abstract
The paper reports an asymptotic expansion for the logarithm of the number of 'log-piles' or 'stacks' which can be built with n congruent circular cylinders. This result has applications to work of Temperley's on the calculation of the entropy of the surfaces of certain crystals. The authors find an asymptotic approximation to the number of graphs on n labelled colored nodes with just q edges for large n and any q. They improve and shorten Liskovec's method to calculate s sub n the number of strong diagraphs on n labelled nodes and deduce the asymptotic expansion of s sub n for large n. The results can be extended to deal with s sub n1, the number of strong diagraphs on n labelled nodes with just q edges. They have extended some asymptotic results of Harary and Read about tree-like polyhexes. Four research papers are printed as appendices to the report. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1971
- Accession Number
- AD0727727
Entities
People
- E. M. Wright
Organizations
- University of Aberdeen