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Keywords:
3-configuration; generating edge set; edge basis; buildup (generating, regulated); bridge
3-configuration; generating edge set; edge basis; buildup (generating, regulated); bridge
Summary:
We deal with two types of buildups of 3-configurations: a generating buildup over a given edge set and a regulated one (according to maximal relative degrees of vertices over a penetrable set of vertices). Then we take account to minimal generating edge sets, i.e., to edge bases. We also deduce the fundamental relation between the numbers of all vertices, of all edges from edge basis and of all terminal elements. The topic is parallel to a certain part of Belousov' “Configurations in algebraic nets” edited in 1979. We attempt to find an apparatus, which, beside others, will decode some less readible chapters of the monograph [1], and which can be useful by further study of 3-configurations with simple edge bases and of corresponding quasigroup identities.
References:
[1] Belousov V. D.: Configurations in algebraic nets. (in Russian), Kishinev (1979). MR 0544665
[2] Krapež A., Taylor M. A.: Bases of web configuration. Publ. de l’ Inst. Math. Beograd, 38 (1985), 21–30. MR 0837378
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