# Regulated buildups of 3-configurations

Archivum Mathematicum (1994)

- Volume: 030, Issue: 1, page 17-24
- ISSN: 0044-8753

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topHavel, Václav J.. "Regulated buildups of 3-configurations." Archivum Mathematicum 030.1 (1994): 17-24. <http://eudml.org/doc/247555>.

@article{Havel1994,

abstract = {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.},

author = {Havel, Václav J.},

journal = {Archivum Mathematicum},

keywords = {3-configuration; generating edge set; edge basis; buildup (generating; regulated); bridge; generating edge set; bridge; buildups; 3-configurations; edge basis},

language = {eng},

number = {1},

pages = {17-24},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Regulated buildups of 3-configurations},

url = {http://eudml.org/doc/247555},

volume = {030},

year = {1994},

}

TY - JOUR

AU - Havel, Václav J.

TI - Regulated buildups of 3-configurations

JO - Archivum Mathematicum

PY - 1994

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 030

IS - 1

SP - 17

EP - 24

AB - 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.

LA - eng

KW - 3-configuration; generating edge set; edge basis; buildup (generating; regulated); bridge; generating edge set; bridge; buildups; 3-configurations; edge basis

UR - http://eudml.org/doc/247555

ER -

## References

top- Belousov V. D., Configurations in algebraic nets, (in Russian), Kishinev (1979). (1979) MR0544665
- Krapež A., Taylor M. A., Bases of web configuration, Publ. de l’ Inst. Math. Beograd, 38 (1985), 21–30. (1985) MR0837378

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