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

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

DOI: https://doi.org/10.1016/j.endm.2017.06.029

Abstract

We establish a lower bound of 10.271 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.

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