The Cyclically Resolvable Steiner Triple Systems of Order 57
A resolution of a Steiner triple system of order <i>v</i> (STS(<i>v</i>)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(<i>v</i>) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable S...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/212 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588101357142016 |
|---|---|
| author | Svetlana Topalova Stela Zhelezova |
| author_facet | Svetlana Topalova Stela Zhelezova |
| author_sort | Svetlana Topalova |
| collection | DOAJ |
| description | A resolution of a Steiner triple system of order <i>v</i> (STS(<i>v</i>)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(<i>v</i>) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable STS(<i>v</i>)s have important applications in Coding Theory. They have been classified up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>=</mo><mn>45</mn></mrow></semantics></math></inline-formula> and before the present work <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>=</mo><mn>57</mn></mrow></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-f418b72f344a4fc5ac1179d3c005043d |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-f418b72f344a4fc5ac1179d3c005043d2025-01-24T13:39:45ZengMDPI AGMathematics2227-73902025-01-0113221210.3390/math13020212The Cyclically Resolvable Steiner Triple Systems of Order 57Svetlana Topalova0Stela Zhelezova1Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaInstitute of Mathematics and Informatics, Bulgarian Academy of Sciences, 1113 Sofia, BulgariaA resolution of a Steiner triple system of order <i>v</i> (STS(<i>v</i>)) is point-cyclic if it has an automorphism permuting the points in one cycle. An STS(<i>v</i>) is cyclically resolvable if it has at least one point-cyclic resolution. Cyclically resolvable STS(<i>v</i>)s have important applications in Coding Theory. They have been classified up to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>=</mo><mn>45</mn></mrow></semantics></math></inline-formula> and before the present work <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>v</mi><mo>=</mo><mn>57</mn></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/13/2/212Steiner triple systemcyclically resolvableautomorphismpoint-cyclic resolutionanti-Paschanti-mitre |
| spellingShingle | Svetlana Topalova Stela Zhelezova The Cyclically Resolvable Steiner Triple Systems of Order 57 Mathematics Steiner triple system cyclically resolvable automorphism point-cyclic resolution anti-Pasch anti-mitre |
| title | The Cyclically Resolvable Steiner Triple Systems of Order 57 |
| title_full | The Cyclically Resolvable Steiner Triple Systems of Order 57 |
| title_fullStr | The Cyclically Resolvable Steiner Triple Systems of Order 57 |
| title_full_unstemmed | The Cyclically Resolvable Steiner Triple Systems of Order 57 |
| title_short | The Cyclically Resolvable Steiner Triple Systems of Order 57 |
| title_sort | cyclically resolvable steiner triple systems of order 57 |
| topic | Steiner triple system cyclically resolvable automorphism point-cyclic resolution anti-Pasch anti-mitre |
| url | https://www.mdpi.com/2227-7390/13/2/212 |
| work_keys_str_mv | AT svetlanatopalova thecyclicallyresolvablesteinertriplesystemsoforder57 AT stelazhelezova thecyclicallyresolvablesteinertriplesystemsoforder57 AT svetlanatopalova cyclicallyresolvablesteinertriplesystemsoforder57 AT stelazhelezova cyclicallyresolvablesteinertriplesystemsoforder57 |