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arXiv · 2003.10743

Atomicity and well quasi-order for consecutive orderings on words and permutations

Matthew McDevitt·Nik Ruskuc
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Abstract

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 characterisations of atomicity and well quasi-order for the subpath ordering on paths of a finite directed graph.

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Matthew McDevitt, Nik Ruskuc. 2020-03-24. Atomicity and well quasi-order for consecutive orderings on words and permutations. https://arxiv.org/abs/2003.10743

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