The enumeration of three pattern classes using monotone grid classes

Albert, M. H.; Atkinson, M. D. and Brignall, Robert (2012). The enumeration of three pattern classes using monotone grid classes. Electronic Journal of Combinatorics, 19(3) P20.

URL: http://www.combinatorics.org/ojs/index.php/eljc/ar...

Abstract

The structure of the three pattern classes defined by the sets of forbidden permutations 2143,4321, 2143,4312 and 1324,4312 is determined using the machinery of monotone grid classes. This allows the permutations in these classes to be described in terms of simple diagrams and regular languages and, using this, the rational generating functions which enumerate these classes are determined.

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