Enumerating Steiner triple systems

Daniel Heinlein; Patric R.J. Östergård

doi:10.1002/jcd.21906

Enumerating Steiner triple systems

Daniel Heinlein^*
, Patric R.J. Östergård

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

2 Sitaatiot (Scopus)

142 Lataukset (Pure)

Abstrakti

Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.

Alkuperäiskieli	Englanti
Sivut	479-495
Sivumäärä	17
Julkaisu	Journal of Combinatorial Designs
Vuosikerta	31
Numero	10
Varhainen verkossa julkaisun päivämäärä	2023
DOI - pysyväislinkit	https://doi.org/10.1002/jcd.21906
Tila	Julkaistu - lokak. 2023
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

The authors thank the referees for their valuable comments. Supported by the Academy of Finland, Grant 331044.

Pääsy asiakirjaan

10.1002/jcd.21906Lisenssi: CC BY

J of Combinatorial Designs - 2023 - HeinleinFinal published version, 632 KBLisenssi: CC BY

Muut tiedostot ja linkit

Linkki julkaisuun Scopuksessa

SubspaceCodes: Constructions and Classifications of Subspace Codes and Related Structures for Communication Networks
Heinlein, D. (Vastuullinen johtaja)
01/09/2020 → 31/08/2023
Projekti: RCF Postdoctoral Researcher

Siteeraa tätä

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title = "Enumerating Steiner triple systems",

abstract = "Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.",

keywords = "classification, counting, regular graph, Steiner triple system",

author = "Daniel Heinlein and {\"O}sterg{\aa}rd, \{Patric R.J.\}",

note = "Funding Information: The authors thank the referees for their valuable comments. Supported by the Academy of Finland, Grant 331044. Publisher Copyright: {\textcopyright} 2023 The Authors. Journal of Combinatorial Designs published by Wiley Periodicals LLC.",

year = "2023",

month = oct,

doi = "10.1002/jcd.21906",

language = "English",

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T1 - Enumerating Steiner triple systems

AU - Heinlein, Daniel

AU - Östergård, Patric R.J.

N1 - Funding Information: The authors thank the referees for their valuable comments. Supported by the Academy of Finland, Grant 331044. Publisher Copyright: © 2023 The Authors. Journal of Combinatorial Designs published by Wiley Periodicals LLC.

PY - 2023/10

Y1 - 2023/10

N2 - Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.

AB - Steiner triple systems (STSs) have been classified up to order 19. Earlier estimations of the number of isomorphism classes of STSs of order 21, the smallest open case, are discouraging as for classification, so it is natural to focus on the easier problem of merely counting the isomorphism classes. Computational approaches for counting STSs are here considered and lead to an algorithm that is used to obtain the number of isomorphism classes for order 21: 14,796,207,517,873,771.

KW - classification

KW - counting

KW - regular graph

KW - Steiner triple system

UR - https://www.scopus.com/pages/publications/85165175156

U2 - 10.1002/jcd.21906

DO - 10.1002/jcd.21906

M3 - Article

AN - SCOPUS:85165175156

SN - 1063-8539

VL - 31

SP - 479

EP - 495

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

IS - 10

ER -

Enumerating Steiner triple systems

Abstrakti

Rahoitus

Pääsy asiakirjaan

Muut tiedostot ja linkit

Sormenjälki

Projektit

SubspaceCodes: Constructions and Classifications of Subspace Codes and Related Structures for Communication Networks

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