Frame self-orthogonal Mendelsohn triple systems of type |
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| Authors: | Yunqing Xu Yanxun Chang Gennian Ge Hantao Zhang |
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| Institution: | aDepartment of Mathematics, Ningbo University, Ningbo, 315211 Zhejiang, China;bDepartment of Mathematics, Beijing Jiaotong University, Beijing 100044, China;cDepartment of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, China;dComputer Science Department, The University of Iowa, Iowa City, IA 52242, USA |
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| Abstract: | A Mendelsohn triple system (MTS) corresponds to an idempotent semisymmetric Latin square (quasigroup) of the same order. A holey MTS is called frame self-orthogonal, briefly FSOMTS, if its associated holey semisymmetric Latin square is frame self-orthogonal. In this paper, we use FSOMTS(hn) to denote an FSOMTS with n spanning holes of size h. The existence of FSOMTS(hn) for h 3 has been known with a few exceptions. We extend the existing results and determine the necessary and sufficient conditions for the existence of FSOMTS(hn) for any h and n with some possible exceptions. |
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| Keywords: | Mendelsohn triple system Latin square Quasigroup Self-orthogonal |
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