Abstract
It is known that the “pattern containment” order on permutations is not a partial well-order. Nevertheless, many naturally defined subsets of permutations are partially well-ordered, in which case they have a strong finite basis property. Several classes are proved to be partially well-ordered under pattern containment. Conversely, a number of new antichains are exhibited that give some insight as to where the boundary between partially well-ordered and not partially well-ordered classes lies.
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Atkinson, M.D., Murphy, M.M. & Ruškuc, N. Partially Well-Ordered Closed Sets of Permutations. Order 19, 101–113 (2002). https://doi.org/10.1023/A:1016500300436
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DOI: https://doi.org/10.1023/A:1016500300436