The existence of large sets of Kirkman triple systems (LKTSs) is one of the best-known open problems in combinatorial design theory. Steiner quadruple systems with resolvable derived designs (RDSQSs) play an important role in the recursive constructions of LKTSs. In this paper, we introduce a special combinatorial structure \(\hbox {RDSQS}^{*}(v)\) and use it to present a construction for RDSQS(4v). As a consequence, some new infinite families of LKTSs are given.

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有关大型柯克曼三重系统的更多结果

大型柯克曼三重系统 (LKTS) 集合的存在是组合设计理论中最著名的开放问题之一。具有可解析派生设计 (RDSQS) 的 Steiner 四元组系统在 LKTS 的递归构造中发挥着重要作用。在本文中，我们引入了一种特殊的组合结构\(\hbox {RDSQS}^{*}(v)\)并用它来呈现 RDSQS(4 v )的构造。因此，给出了一些新的无限 LKTS 族。