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- W2079252521 abstract "Denniston (J. Combin. Theory Ser. A 26 (1979) 298) presented a tripling construction for large sets of Kirkman triple systems (LKTS) under the condition that there exists a transitive Kirkman triple system (TKTS). In this paper, we first define a transitive resolvable idempotent symmetric quasigroup (TRISQ), and show that a TRISQ of order v always exists for any positive integer v≡3(mod6). Then, we present a tripling construction of LKTS by using TRISQ instead of TKTS. Hence the condition “there exists a TKTS” in Denniston's tripling construction can be removed." @default.
- W2079252521 created "2016-06-24" @default.
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- W2079252521 date "2002-03-01" @default.
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- W2079252521 title "Transitive resolvable idempotent symmetric quasigroups and large sets of Kirkman triple systems" @default.
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- W2079252521 doi "https://doi.org/10.1016/s0012-365x(01)00178-9" @default.
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