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Kirkman triple systems with subsystems

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  • Janne Kokkala
  • Patric R. J. Ostergard

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 (mod 6). 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. (C) 2020 Elsevier B.V. All rights reserved.

OriginalsprogEngelsk
Artikelnummer111960
TidsskriftDiscrete Mathematics
Vol/bind343
Udgave nummer9
Antal sider8
ISSN0012-365X
DOI
StatusUdgivet - 2020
Eksternt udgivetJa

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