Sparse Steiner triple systems of order 21
(2021) In Journal of Combinatorial Designs 29(2). p.75-83- 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... (More)
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.
(Less)
- author
- Kokkala, Janne I. LU and Östergård, Patric R.J.
- organization
- publishing date
- 2021-02
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- automorphism group, Kirkman triple system, Pasch configuration, quadrilateral, Steiner triple system
- in
- Journal of Combinatorial Designs
- volume
- 29
- issue
- 2
- pages
- 9 pages
- publisher
- John Wiley & Sons Inc.
- external identifiers
-
- scopus:85096683887
- ISSN
- 1063-8539
- DOI
- 10.1002/jcd.21757
- language
- English
- LU publication?
- yes
- id
- 19fdb21b-9937-43c0-8625-05eeb1bca045
- date added to LUP
- 2020-12-08 14:19:46
- date last changed
- 2022-05-04 22:01:08
@article{19fdb21b-9937-43c0-8625-05eeb1bca045,
abstract = {{<p>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.</p>}},
author = {{Kokkala, Janne I. and Östergård, Patric R.J.}},
issn = {{1063-8539}},
keywords = {{automorphism group; Kirkman triple system; Pasch configuration; quadrilateral; Steiner triple system}},
language = {{eng}},
number = {{2}},
pages = {{75--83}},
publisher = {{John Wiley & Sons Inc.}},
series = {{Journal of Combinatorial Designs}},
title = {{Sparse Steiner triple systems of order 21}},
url = {{http://dx.doi.org/10.1002/jcd.21757}},
doi = {{10.1002/jcd.21757}},
volume = {{29}},
year = {{2021}},
}