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This article is cited in 11 scientific papers (total in 12 papers)
Partial geometries and their extensions
A. A. Makhnev Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
This survey consists of three parts: partial geometries, diagram geometries, and extensions of partial geometries. In the first part we present the main definitions, all known examples of partial geometries, some characterization theorems, and also certain results on semipartial geometries. In the second part we give definitions related to geometries belonging to diagrams, a series of general results concerning these geometries, examples of rank 2 geometries that play the role of building blocks for geometries of higher rank, and also theorems on the structure of some flag-transitive rank 2 geometries. In the third part we give a survey of results characterizing extensions of partial geometries, namely, 2-designs and dual 2-designs, nets and dual nets, and also generalized quadrangles. Moreover, in the concluding subsection of this part we present some generalizations of the notion of extension and the corresponding characterization results.
Received: 26.04.1999
Citation:
A. A. Makhnev, “Partial geometries and their extensions”, Uspekhi Mat. Nauk, 54:5(329) (1999), 25–76; Russian Math. Surveys, 54:5 (1999), 895–945
Linking options:
https://www.mathnet.ru/eng/rm203https://doi.org/10.1070/rm1999v054n05ABEH000203 https://www.mathnet.ru/eng/rm/v54/i5/p25
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Abstract page: | 653 | Russian version PDF: | 332 | English version PDF: | 25 | References: | 70 | First page: | 1 |
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