Abstract
A simple \((2,3,v)\) trade is a pair \((T_0,T_1)\) of disjoint sets of \(3\)-subsets (blocks) of a \(v\)-set such that any two elements meet the same number of times in the blocks of \(T_0\) and the blocks of \(T_1\). The size of \(T_0\) equals the size of \(T_1\) and is called the volume of the trade. In this paper, for \(v=4n+2\), we introduce a new partitioning of the set of all 3-subsets of a v-set into the trades of volume \(4\), \(6\), and \(8\).
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Acknowledgements
The authors thank Professor Denis Krotov of Sobolev Institute of Mathematics for mentioning the paper by Sauskan and Tarannikov [12]. We would like to express our gratitude to editors and referees for their kind suggestions.
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Communicated by L. Teirlinck.
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Ahmadi, M.H., Akhlaghinia, N., Khosrovshahi, G.B. et al. New partitionings of complete designs. Des. Codes Cryptogr. 89, 2715–2723 (2021). https://doi.org/10.1007/s10623-021-00950-z
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DOI: https://doi.org/10.1007/s10623-021-00950-z