Atomicity and well quasi-order for consecutive orderings on words and permutations
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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.
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
SIAM Journal on Discrete Mathematics
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