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

KTH Royal Institute of Technology

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

10 Sitaatiot (Scopus)

260 Lataukset (Pure)

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
Sivumäärä	8
Julkaisu	Discrete Mathematics
Vuosikerta	343
Numero	9
DOI - pysyväislinkit	https://doi.org/10.1016/j.disc.2020.111960
Tila	Julkaistu - syysk. 2020
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

Supported in part by the Academy of Finland, Grant No. 289002. The first author was also supported in part by the Swedish Research Council grant 2016-00782.

Pääsy asiakirjaan

10.1016/j.disc.2020.111960

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

Muut tiedostot ja linkit

Link to publication in Scopus

Kirkman triple systems with subsystems
Kokkala, J. (Creator) & Östergård, P. (Creator), Zenodo, 29 elok. 2019
DOI - pysyväislinkki: 10.5281/zenodo.3699565
Tietoaineisto: Dataset

1 Päättynyt

Konstruktion och klassificering av diskreta matematiska strukturer
Östergård, P. (Vastuullinen johtaja), Ganzhinov, M. (Projektin jäsen), Szollosi, F. (Projektin jäsen), Heinlein, D. (Projektin jäsen), Kokkala, J. (Projektin jäsen), Pöllänen, A. (Projektin jäsen), Laaksonen, A. (Projektin jäsen) & Paavola, W. (Projektin jäsen)
01/09/2015 → 31/08/2019
Projekti: Academy of Finland: Other research funding

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title = "Kirkman triple systems with subsystems",

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.",

keywords = "Automorphism group, Doubly resolvable, Kirkman triple system, Resolution, Steiner triple system, Subsystem",

author = "Kokkala, \{Janne I.\} and {\"O}sterg{\aa}rd, \{Patric R.J.\}",

year = "2020",

month = sep,

doi = "10.1016/j.disc.2020.111960",

language = "English",

volume = "343",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "9",

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TY - JOUR

T1 - Kirkman triple systems with subsystems

AU - Kokkala, Janne I.

AU - Östergård, Patric R.J.

PY - 2020/9

Y1 - 2020/9

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/85084580922

U2 - 10.1016/j.disc.2020.111960

DO - 10.1016/j.disc.2020.111960

M3 - Article

AN - SCOPUS:85084580922

SN - 0012-365X

VL - 343

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 9

M1 - 111960

ER -

Kirkman triple systems with subsystems

Abstrakti

Rahoitus

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Tietoaineistot

Kirkman triple systems with subsystems

Projektit

Konstruktion och klassificering av diskreta matematiska strukturer

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