Kirkman triple systems with subsystems

Janne I. Kokkala; Patric R.J. Östergård

doi:10.1016/j.disc.2020.111960

Kirkman triple systems with subsystems

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

Abstrakti

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.

Alkuperäiskieli	Englanti
Artikkeli	111960
Julkaisu	Discrete Mathematics
Vuosikerta	343
Numero	9
DOI - pysyväislinkit	https://doi.org/10.1016/j.disc.2020.111960
Tila	Julkaistu - syyskuuta 2020
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1016/j.disc.2020.111960

Link to publication in Scopus

Kielletty (embargo) dokumentti

Kokkala_Kirkman_triple_systems_DiMath
Accepted author manuscript, 109 KB
Lisenssi: CC BY-NC-ND
Kielto päättyy: 15/05/2022

Sormenjälki Sukella tutkimusaiheisiin 'Kirkman triple systems with subsystems'. Ne muodostavat yhdessä ainutlaatuisen sormenjäljen.

Projektit

1 Päättynyt

Konstruktion och klassificering av diskreta matematiska strukturer

Kokkala, J., Laaksonen, A., Heinlein, D., Ganzhinov, M., Östergård, P. & Szollosi, F.

01/09/2015 → 24/09/2019

Projekti: Academy of Finland: Other research funding

Siteeraa tätä

Kokkala, J. I., & Östergård, P. R. J. (2020). Kirkman triple systems with subsystems. Discrete Mathematics, 343(9), [111960]. https://doi.org/10.1016/j.disc.2020.111960

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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.

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