Grid classes and partial well order

Authors:
Robert Brignall
Affiliations:
Department of Mathematics and Statistics, The Open University, Milton Keynes, UK
Venue:
Journal of Combinatorial Theory Series A
Year:
2012

Citing 4
Cited 0

Minimal antichains in well-founded quasi-orders with an application to tournaments

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Excluded permutation matrices and the Stanley-Wilf conjecture

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Graph Minors. XX. Wagner's conjecture

Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Decomposing simple permutations, with enumerative consequences

Combinatorica

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Abstract

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.