The Cyclically Resolvable Steiner Triple Systems of Order 57

Svetlana Topalova and Stela Zhelezova ()
Additional contact information
Svetlana Topalova: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria
Stela Zhelezova: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 2, 1-13

Abstract: A resolution of a Steiner triple system of order v (STS( v )) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS( v ) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable STS( v )s have important applications in Coding Theory. They have been classified up to v = 45 and before the present work v = 57 was the first open case. There are 2,353,310 cyclic STS(57)s. We establish that 155,966 of them are cyclically resolvable yielding 3,638,984 point-cyclic resolutions which we classify with respect to their automorphism groups and to the availability of some configurations.

Keywords: Steiner triple system; cyclically resolvable; automorphism; point-cyclic resolution; anti-Pasch; anti-mitre; 5-sparse (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/2/212/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/2/212/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:2:p:212-:d:1563983

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().