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Enumeration of Large Combinatorial Structures.

Author: Edward M Wright; ABERDEEN UNIV (Scotland)
Publisher: Ft. Belvoir Defense Technical Information Center NOV 1977.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
New results are given about the number of 2-connected labelled (n, q) graphs, i.e. graphs on n points and q lines, including a combinatorial interpretation of Temperley's differential equation satisfied by the exponential generating function of this number (applicable in Statistical Mechanics). This leads to two methods for finding asymptotic approximations to this number. A curious paradox is found in the  Read more...
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Document Type: Book
All Authors / Contributors: Edward M Wright; ABERDEEN UNIV (Scotland)
OCLC Number: 227484519
Description: 52 p.

Abstract:

New results are given about the number of 2-connected labelled (n, q) graphs, i.e. graphs on n points and q lines, including a combinatorial interpretation of Temperley's differential equation satisfied by the exponential generating function of this number (applicable in Statistical Mechanics). This leads to two methods for finding asymptotic approximations to this number. A curious paradox is found in the asymptotic enumeration of unlabelled graphs. Work was continued on connected, sparsely-edged graphs of various kinds, again including asymptotic results with possible applications. Finally a new ghost expansion method is described to obtain asymptotic results from the Exclusion-Inclusion Theorem by applying the method to a particular graphical example. The appendices consist of four research papers which have been submitted for publication to different mathematical journals.

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