Grid classes and partial well order

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 ...

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On Partial Well-Order for Monotone Grid Classes of Permutations

The permutation π of [n] = {1, 2, . . . , n} contains the permutation σ of [k] = {1, 2, . . . , k} (written σ ≤ π) if π has a subsequence of length k order isomorphic to σ. For example, π = 391867452 (written in list, or one-line notation) contains σ = 51342, as can be seen by considering the subsequence 91672 (= π(2), π(3), π(5), π(6), π(9)). A permutation class is a downset of permutations un...

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’ s repository of research publications and other research outputs Grid classes and partial well order

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 ...

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research publications and other research outputs Grid classes and partial well order

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 ...

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University ’ s repository of research publications and other research outputs Grid classes and partial well order

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 ...

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Grid classes and partial well order

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