SIAM Journal on Discrete Mathematics, Volume 35, Issue 1, Page 495-520, January 2021.
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are (a) being atomic, i.e., not being decomposable as a union of two downward closed proper subsets or, equivalently, satisfying the joint embedding property; and (b) being well quasi-ordered. The two posets are (1) words over a finite alphabet under the consecutive subword ordering, and (2) finite permutations under the consecutive subpermutation ordering. Underpinning the four results are characterizations of atomicity and well quasi-order for the subpath ordering on paths of a finite directed graph.

中文翻译：

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单词和排列的连续排序的原子性和井准顺序

SIAM 离散数学杂志，第 35 卷，第 1 期，第 495-520 页，2021 年 1 月。
为由两个无限偏序组中的有限多个障碍物定义的向下封闭子集的两个阶理论性质建立了算法可判定性。所考虑的特性是 (a) 是原子的，即不能分解为两个向下封闭的真子集的并集，或者等价地满足联合嵌入特性；(b) 准有序。这两个偏序集是 (1) 连续子词排序下的有限字母表上的单词，以及 (2) 连续子排列排序下的有限排列。支持这四个结果的是有限有向图路径上子路径排序的原子性和井准顺序的表征。