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Abstract
A geometric grid class consists of those permutations that can be drawn on a specified set of line segments of slope ±1 arranged in a rectangular pattern governed by a matrix. Using a mixture of geometric and language theoretic methods, we prove that such classes are specified by finite sets of forbidden
permutations, are partially well ordered, and have rational generating functions. Furthermore, we show that these properties are inherited by the subclasses (under permutation involvement) of such classes, and establish the basic lattice theoretic properties of the collection of all such subclasses.
permutations, are partially well ordered, and have rational generating functions. Furthermore, we show that these properties are inherited by the subclasses (under permutation involvement) of such classes, and establish the basic lattice theoretic properties of the collection of all such subclasses.
| Original language | English |
|---|---|
| Pages (from-to) | 5859-5881 |
| Number of pages | 23 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 365 |
| Issue number | 11 |
| Early online date | 25 Apr 2013 |
| DOIs | |
| Publication status | Published - Nov 2013 |
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Dive into the research topics of 'Geometric grid classes of permutations'. Together they form a unique fingerprint.Projects
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The Structure of Permutation Classes: The Structure of Permutation Classes
Ruskuc, N. (PI)
21/10/11 → 20/10/14
Project: Standard