最小素数年龄、字与置换图
Minimal prime ages, words and permutation graphs Extended abstract
摘要：
本文是对有限图遗传类研究的一个贡献。我们根据它们所包含的素数结构的数量对这些类进行分类。我们考虑这样的类是\emph{minimal prime}：类包含无穷多个素数，但每个正常的遗传子类只包含1000多个素数。我们给这样的类的一个完整的特征。事实上，这些类中的每一个都是一个良好的准序年龄，并且有无数个。这些年龄的11个保持良好的准有序时，标签在一个良好的准序。在其余的，可数许多保持良好的准有序时，一个标签添加。除了六个例子，这些年龄的成员，我们刻画的置换图。事实上，不属于这11个1的每个年龄都是与整数上的一致递归$0$ - $1$字相关联的图的年龄。给出了偏序集和双链的极小素类的一个刻画。
英文摘要：
This paper is a contribution to the study of hereditary classes of finite graphs. We classify these classes according to the number of prime structures they contain. We consider such classes that are \emph{minimal prime}: classes that contain infinitely many primes but every proper hereditary subclass contains only finitely many primes. We give a complete characterization of such classes. In fact, each one of these classes is a well quasi ordered age and there are uncountably many of them. Eleven of these ages remain well quasi ordered when labels in a well quasi ordering are added. Among the remaining ones, countably many remain well quasi ordered when one label is added. Except for six examples, members of these ages we characterize are permutation graphs. In fact, every age which is not among the eleven ones is the age of a graph associated to a uniformly recurrent $0$-$1$ word on the integers. A characterization of minimal prime classes of posets and bichains is also provided.
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