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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 (fromto)  58595881 
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
 1 Finished

The Structure of Permutation Classes: The Structure of Permutation Classes
21/10/11 → 20/10/14
Project: Standard