Sparse Steiner triple systems of order 21

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Author
Date
2021-02
Department
Department of Communications and Networking
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Mcode
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Language
en
Pages
9
Series
Journal of Combinatorial Designs
Abstract
A (Formula presented.) -configuration is a set of (Formula presented.) blocks on (Formula presented.) points. For Steiner triple systems, (Formula presented.) -configurations are of particular interest. The smallest nontrivial such configuration is the Pasch configuration, which is a (Formula presented.) -configuration. A Steiner triple system of order (Formula presented.), an STS (Formula presented.), is (Formula presented.) -sparse if it does not contain any (Formula presented.) -configuration for (Formula presented.). The existence problem for anti-Pasch Steiner triple systems has been solved, but these have been classified only up to order 19. In the current work, a computer-aided classification shows that there are 83,003,869 isomorphism classes of anti-Pasch STS(21)s. Exploration of the classified systems reveals that there are three 5-sparse STS(21)s but no 6-sparse STS(21)s. The anti-Pasch STS(21)s lead to 14 Kirkman triple systems, none of which is doubly resolvable.
Description
Keywords
automorphism group, Kirkman triple system, Pasch configuration, quadrilateral, Steiner triple system
Other note
DOI
10.1002/jcd.21757
Citation
Kokkala, J I & Östergård, P R J 2021, ' Sparse Steiner triple systems of order 21 ', Journal of Combinatorial Designs, vol. 29, no. 2, pp. 75-83 . https://doi.org/10.1002/jcd.21757
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https://urn.fi/URN:NBN:fi:aalto-2020123160356
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[article-cris] Sähkötekniikan korkeakoulu / ELEC