Geodesic
A~threshold function with the Shannon effect for Boolean functions with respect to a~symmetric group
Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 64-75.

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We prove that if $A$ is the property of a Boolean function $f(x_1,\dots,x_n)$ of weight $r$ consisting in the fact that $f$ has a trivial inertia group with respect to the group $S_n$, then the function $A(n)=\ln n$ is a threshold function for property $A$. 
@article{DM_1993_5_3_a4,
     author = {O. V. Denisov},
     title = {A~threshold function with the {Shannon} effect for {Boolean} functions with respect to a~symmetric group},
     journal = {Diskretnaya Matematika},
     pages = {64--75},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1993_5_3_a4/}
}
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O. V. Denisov. A~threshold function with the Shannon effect for Boolean functions with respect to a~symmetric group. Diskretnaya Matematika, Tome 5 (1993) no. 3, pp. 64-75. http://geodesic.mathdoc.fr/item/DM_1993_5_3_a4/