Abstract
Let \(J^{3}_{R}(v)\) denote the set of all integers k such that there exists a collection of three KTS(v) pairwise intersecting in the same set of k blocks. In this paper for sufficiently large v where \(v\equiv 3\) (mod 6), we determine the set \(J^{3}_{R}(v)\) except possibly for two values \(t_v-10\) and \(t_v-13\), where \(t_v\) is the number of triples contained in KTS(v).
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Acknowledgements
The authors of this article would like to acknowledge Professor E. S. Mahmoodian for his interesting suggestions and his useful comments. We are also thankful to Mr. A. Khosroshahi and Mr. M. Hasanvand for helping us to find small cases, with the computer programming. And last but not least we would like to express our appreciation to Ms. S. Golalizadeh and Mr. A. Chegini for their very beneficial discussions and their interest in our work.
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Amjadi, H., Soltankhah, N. The 3-Way Intersection Problem for Kirkman Triple Systems. Graphs and Combinatorics 33, 673–687 (2017). https://doi.org/10.1007/s00373-017-1801-8
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DOI: https://doi.org/10.1007/s00373-017-1801-8