Geometric grid classes of permutations
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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.
Albert , M H , Atkinson , M D , Bouvel , M , Ruskuc , N & Vatter , V 2013 , ' Geometric grid classes of permutations ' Transactions of the American Mathematical Society , vol. 365 , no. 11 , pp. 5859-5881 . DOI: 10.1090/S0002-9947-2013-05804-7
Transactions of the American Mathematical Society
© Copyright 2013 American Mathematical Society. First published in Transactions of the American Mathematical Society in 365(11) 2013, published by the American Mathematical Society.
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