Kirkman triple systems with subsystems

Janne I. Kokkala; Patric R.J. Östergård

doi:10.1016/j.disc.2020.111960

Kirkman triple systems with subsystems

Janne I. Kokkala, Patric R.J. Östergård

Information Theory

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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.

Original language	English
Article number	111960
Number of pages	8
Journal	Discrete Mathematics
Volume	343
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2020.111960
Publication status	Published - Sep 2020
MoE publication type	A1 Journal article-refereed

Keywords

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

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10.1016/j.disc.2020.111960

Kokkala_Kirkman_triple_systems_DiMathAccepted author manuscript, 109 KBLicence: CC BY-NC-ND

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AB - 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.

KW - Automorphism group

KW - Doubly resolvable

KW - Kirkman triple system

KW - Resolution

KW - Steiner triple system

KW - Subsystem

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Kirkman triple systems with subsystems

Abstract

Keywords

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