Grid classes and partial well order |
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Authors: | Robert Brignall |
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Institution: | Department of Mathematics and Statistics, The Open University, Milton Keynes, UK |
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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. |
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Keywords: | Permutation classes Grid classes Partial well-order Infinite antichains |
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