论文标题
固定均匀的超图
Set-homogeneous hypergraphs
论文作者
论文摘要
a $ k $均匀的超graph $ m $如果可计数（可能是有限的），则每当两个有限的诱导subhypergraphs $ u，v $是同构的，$ u^g = v $;如果有限诱导的亚缩写物之间的每一个同构延伸至自动形态，则据说HyperGraph $ m $均具有同质性。我们给出了四个示例，这些例子是无限的固定$ k $均匀的超图（两个均不均匀的尺寸）（两个带有$ k = 3 $，一个$ k = 4 $，一个$ k = 6 $）。还可以证明这些可能是唯一的互补性。例如，对于$ k = 3 $，只有一个无数$ k $统一的超图，其自动形态组不是2传输，而没有$ k = 4 $。我们还举例说明了有限的固定均匀的3均匀超图，这是不均匀的。
A $k$-uniform hypergraph $M$ is set-homogeneous if it is countable (possibly finite) and whenever two finite induced subhypergraphs $U,V$ are isomorphic there is $g\in Aut(M)$ with $U^g=V$; the hypergraph $M$ is said to be homogeneous if in addition every isomorphism between finite induced subhypergraphs extends to an automorphism. We give four examples of countably infinite set-homogeneous $k$-uniform hypergraphs which are not homogeneous (two with $k=3$, one with $k=4$, and one with $k=6$). Evidence is also given that these may be the only ones, up to complementation. For example, for $k=3$ there is just one countably infinite $k$-uniform hypergraph whose automorphism group is not 2-transitive, and there is none for $k=4$. We also give an example of a finite set-homogeneous 3-uniform hypergraph which is not homogeneous.
