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...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/2/212 |
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| Summary: | 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. |
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| ISSN: | 2227-7390 |