# A structural characterisation of Av(1324) and new bounds on its growth rate

@article{Bevan2020ASC, title={A structural characterisation of Av(1324) and new bounds on its growth rate}, author={David Bevan and Robert Brignall and Andrew Elvey Price and Jay Pantone}, journal={Eur. J. Comb.}, year={2020}, volume={88}, pages={103115} }

We establish an improved lower bound of 10.271 for the exponential growth rate of the class of permutations avoiding the pattern 1324, and an improved upper bound of 13.5. These results depend on a new exact structural characterisation of 1324-avoiders as a subclass of an infinite staircase grid class, together with precise asymptotics of a small domino subclass whose enumeration we relate to West-two-stack-sortable permutations and planar maps. The bounds are established by carefully combining…

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