Atomicity and well quasi-order for consecutive orderings on words and permutations
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.
Citation
McDevitt , M & Ruskuc , N 2021 , ' Atomicity and well quasi-order for consecutive orderings on words and permutations ' , SIAM Journal on Discrete Mathematics , vol. 35 , no. 1 , pp. 495–520 . https://doi.org/10.1137/20M1338411
Publication
SIAM Journal on Discrete Mathematics
Status
Peer reviewed
ISSN
0895-4801Type
Journal article
Rights
Copyright © 2021 Society for Industrial and Applied Mathematics. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1137/20M1338411.
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