Grid classes and partial well order

Date
Authors
Brignall, Robert
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
We prove necessary and sufficient conditions on a family of (generalised) gridding matrices to determine when the corresponding permutation classes are partially well-ordered. One direction requires an application of Higman's Theorem and relies on there being only finitely many simple permutations in the only non-monotone cell of each component of the matrix. The other direction is proved by a more general result that allows the construction of infinite antichains in any grid class of a matrix whose graph has a component containing two or more non-monotone-griddable cells. The construction uses a generalisation of pin sequences to grid classes, together with a number of symmetry operations on the rows and columns of a gridding.
Comment: 22 pages, 7 figures. To appear in J. Comb. Theory Series A
Keywords
Mathematics - Combinatorics
Citation
Collections