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%display latex 
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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 $32541$.

In [3]:
S = Specification([],[[2,1,4,3,6,5],[3,4,1,2],[5,2,1,4,3],[3,2,5,4,1]])
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S
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S.solve()
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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).

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S.concrete()
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We can now sample close to the radius of convergence, which is the same as that of $\mathcal X$.

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C = S.sampler(0.29, formal=True)
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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

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list_plot(perm1,aspect_ratio=1,dpi=50)
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list_plot(perm2,aspect_ratio=1,dpi=50)
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list_plot(perm3,aspect_ratio=1,dpi=50)
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We see below that permutations in $\mathcal T_3$ converge to the $X$-permuton.

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list_plot(C.run(10,family=3),aspect_ratio=1,dpi=50)
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