An improved product construction for large sets of Kirkman triple systems |
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Authors: | S. Zhang L. Zhu |
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Affiliation: | a Department of Mathematics, Fujian Teachers University, Fuzhou 350007, People's Republic of China b Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China |
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Abstract: | It has been shown by Lei, in his recent paper, that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS(v) is a transitive Kirkman triple system of order v, and an LR(u) is a new kind of design introduced by Lei. In this paper, we improve this product construction by removing the condition “there exists a TKTS(v)”. Our main idea is to use transitive resolvable idempotent symmetric quasigroups instead of TKTS. As an application, we can combine the known results on LKTS and LR-designs to obtain the existence of an LKTS(3nm(2·13n1+1)(2·13nt+1)) for n1, m{1,5,11,17,25,35,43,67,91,123}{22r+125s+1 : r0,s0}, t0 and ni1 (i=1,…,t). |
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Keywords: | LR-design Large set of Kirkman triple systems Transitive resolvable idempotent symmetric quasigroup |
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