%display latex
load("../specifier.py")
We work here with the class $\oplus[\mathcal X,\mathcal X] \cup \mathcal X$, where $\mathcal X$ is the X-class (see the corresponding Jupyter notebook). This class can be alternatively characterised as the class of separable permutations that avoid $214365$, $3412$, $52143$ and $32541$.
S = Specification([],[[2,1,4,3,6,5],[3,4,1,2],[5,2,1,4,3],[3,2,5,4,1]])
S
S.solve()
The critical families are $\mathcal T_0,\mathcal T_3,\mathcal T_4,\mathcal T_5,\mathcal T_7,\mathcal T_8$. The families $\mathcal T_3,\mathcal T_5,\mathcal T_7,\mathcal T_8$ form a strongly connected component, in which each family converges to the X-permuton. (actually all of those are subfamilies of $\mathcal X$ with minor restrictions, see below).
S.concrete()
We can now sample close to the radius of convergence, which is the same as that of $\mathcal X$.
C = S.sampler(0.29, formal=True)
perm1,perm2,perm3 = C.run(10),C.run(10),C.run(10)
We see below that the limit shape is a random block-diagonal composition of two $X$'s
list_plot(perm1,aspect_ratio=1,dpi=50)
list_plot(perm2,aspect_ratio=1,dpi=50)
list_plot(perm3,aspect_ratio=1,dpi=50)
We see below that permutations in $\mathcal T_3$ converge to the $X$-permuton.
list_plot(C.run(10,family=3),aspect_ratio=1,dpi=50)