Kirkman triple systems with subsystems

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2020-09
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
Discrete Mathematics, Volume 343, issue 9
Abstract
A Steiner triple system of order v, STS(v), together with a resolution of its blocks is called a Kirkman triple system of order v, KTS(v). A KTS(v) exists if and only if v≡3(mod6). The smallest order for which the KTS(v) have not been classified is v=21, which is also the smallest order for which the existence of a doubly resolvable STS(v) is open. Here, KTS(21) with STS(7) and STS(9) subsystems are classified, leading to more than 13 million KTS(21). In this process, systems missing from an earlier classification of KTS(21) with nontrivial automorphisms are encountered, so such a classification is redone.
Description
Keywords
Automorphism group, Doubly resolvable, Kirkman triple system, Resolution, Steiner triple system, Subsystem
Other note
Citation
Kokkala, J I & Östergård, P R J 2020, ' Kirkman triple systems with subsystems ', Discrete Mathematics, vol. 343, no. 9, 111960 . https://doi.org/10.1016/j.disc.2020.111960