, Volume 19, Issue 2, pp 101-113

Partially Well-Ordered Closed Sets of Permutations

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.