Kirkman triple systems with subsystems

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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2020-09

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Department of Communications and Networking

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Language

en

Pages

8

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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.

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Keywords

Automorphism group, Doubly resolvable, Kirkman triple system, Resolution, Steiner triple system, Subsystem

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DOI

10.1016/j.disc.2020.111960

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

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https://urn.fi/URN:NBN:fi:aalto-202006013454

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[article-cris] Sähkötekniikan korkeakoulu / ELEC