Characterization of affine Steiner triple systems and Hall triple systems |
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| Affiliation: | 1. Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Islamic Republic of Iran;2. Department of Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Kashan, Kashan 87317-51167, Islamic Republic of Iran;1. Center for Combinatorics and LPMC-TJKLC Nankai University, Tianjin 300071, China;2. Department of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, China;1. Institut für Diskrete Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria;2. Università degli Studi Niccolò Cusano - Via Don Carlo Gnocchi, 3 00166 Roma, Italy |
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| Abstract: | It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner triple system is affine if and only if it does not contain any of these configurations. Similarly, we characterize Hall triple systems, a superclass of affine Steiner triple systems, using two forbidden configurations. |
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