On Stanley-Wilf limit of the pattern 1324

We use the Mansour-Vainshtein theory of kernel shapes [14] to decompose the set S_n(1324) of 1324-avoiding permutations of length n into small pieces that are governed by some kernel shape λ. An enumeration of the set K_m,c of all kernel shapes with length m and capacity c allows to express the generating function for the number of 1324-avoiding permutations of length n in terms of the P_m(C(x))=∑_c|K_m,c+1|C^c(x) where P_m(x) is a polynomial and C(x) is the generating function for the Catalan numbers. This allows us to write down a systematic procedure for finding a lower bound for approximating the Stanley-Wilf limit of the pattern 1324. We use an implementation of this method in the OpenCL framework to compute such a bound explicitly.