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Staircases, dominoes, and the growth rate of 1324-avoiders

Bevan, David and Brignall, Robert and Elvey Price, Andrew and Pantone, Jay (2017) Staircases, dominoes, and the growth rate of 1324-avoiders. Electronic Notes in Discrete Mathematics, 61. 123–129. ISSN 1571-0653

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Abstract

We establish a lower bound of 10.24 for the growth rate of the permutations avoiding 1324, and an upper bound of 13.5. This is done by first finding the precise growth rate of a subclass whose enumeration is related to West-2-stack-sortable permutations, and then combining copies of this subclass in particular ways.