当前位置: X-MOL 学术J. Comb. Des. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Affine Mendelsohn triple systems and the Eisenstein integers
Journal of Combinatorial Designs ( IF 0.7 ) Pub Date : 2020-06-24 , DOI: 10.1002/jcd.21739
Alex W. Nowak 1
Affiliation  

We define a Mendelsohn triple system (MTS) of order coprime with 3, and having multiplication affine over an abelian group, to be affine, nonramified. By exhibiting a one‐to‐one correspondence between isomorphism classes of affine MTS and those of modules over the Eisenstein integers, we solve the isomorphism problem for affine, nonramified MTS and enumerate these isomorphism classes (extending the work of Donovan, Griggs, McCourt, Opršal, and Stanovský). As a consequence, all entropic MTSs of order coprime with 3 and distributive MTS of order coprime with 3 are classified. Partial results on the isomorphism problem for affine MTS with order divisible by 3 are given, and a complete classification is conjectured. We also prove that for any affine MTS, the qualities of being nonramified, pure, and self‐orthogonal are equivalent.

中文翻译:

仿射Mendelsohn三重系统和Eisenstein整数

我们定义一个与3互质的孟德尔森三重系统(MTS),并在一个阿贝尔群上具有仿射,仿射,不分叉。通过展示仿射MTS的同构类与模块在爱森斯坦整数上的同构类之间的一一对应关系,我们解决了仿射,非分枝MTS的同构问题,并列举了这些同构类(扩展了Donovan,Griggs,McCourt, Opršal和Stanovský)。结果,对所有阶数为3的熵MTS和分布阶数为3的分布MTS进行了分类。给出了三阶可仿射仿射MTS同构问题的部分结果,并推测出一个完整的分类。我们还证明,对于任何仿射MTS,非分枝,纯正和自正交的品质是等效的。
更新日期:2020-06-24
down
wechat
bug