Partially Well-Ordered Closed Sets of Permutations

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. Keywords Permutation, pattern containment, involvement, finite basis, partial well-order

• Type: Journal
• Year: 2002
• Where: ORDER
• Authors: Mike D. Atkinson, Max Murphy, Nikola Ruskuc
• Keywords: ORDER 2002, Pattern Containment, Permutation, Well-ordered