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54 papers · 1 filter
Perfect difference families, perfect systems of difference sets and their applications
Hengrui Liu, Tao Feng, Xiaomiao Wang +1
Let be a positive odd integer. A -perfect difference family (PDF) is a collection of -subsets of such that the multiset $\bigcup_…
The existence of pyramidal Steiner triple systems over abelian groups
Yanxun Chang, Tommaso Traetta, Junling Zhou
A Steiner triple system STS is called -pyramidal if it has an automorphism group fixing points and acting sharply transitively on the remaining points. In this pa…
Existence of magic rectangle sets over finite abelian groups
Shikang Yu, Tao Feng, Hengrui Liu
Let , and be positive integers. Let be a finite abelian group of order . A -magic rectangle set MRS is a collection of arrays of size $a\t…
A family of regular polytopes of order with type
Dong-Dong Hou, Ting-Ting Kong, Hai-Peng Qu
In this paper, we construct an infinite families of group of order which can be an automorphism group of some regular polytope with type , where an…
Two-distance transitive normal Cayley graphs
Jun-Jie Huang, Yan-Quan Feng, Jin-Xin Zhou
In this paper, we construct an infinite family of normal Cayley graphs, which are -distance-transitive but neither distance-transitive nor -arc-transitive. This answers a que…
Stability of pair graphs
Yan-Li Qin, Binzhou Xia, Jin-Xin Zhou +1
We start up the study of the stability of general graph pairs. This notion is a generalization of the concept of the stability of graphs. We say that a pair of graphs is st…