The Number of Cyclic Configurations of Type (v3) and the Isomorphism Problem |
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| Authors: | Hiroki Koike István Kovács Tomaž Pisanski |
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| Affiliation: | 1. IAM, University of Primorska Muzejski trg 2, Koper, Slovenia;2. IAM and FAMNIT, University of Primorska Muzejski trg 2, Koper, Slovenia;3. FMF, University of Ljubljana Jadranska 19, Ljubljana, Slovenia |
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| Abstract: | A configuration of points and lines is cyclic if it has an automorphism that permutes its points in a full cycle. A closed formula is derived for the number of nonisomorphic connected cyclic configurations of type (v3), i.e. which have v points and lines, and each point/line is incident with exactly three lines/points. In addition, a Bays–Lambossy type theorem is proved for cyclic configurations if the number of points is a product of two primes or a prime power. |
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| Keywords: | cyclic configuration cyclic object isomorphismMSC 2010: 20B25 51E30 05C25 05C60 |
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