Geodesic
Properties of proper families of Boolean functions
Diskretnaya Matematika, Tome 33 (2021) no. 1, pp. 91-102

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We show that triangular families of Boolean functions comprise an exponentially small fraction of proper families of a given order. We prove that if $F$ is a proper family of Boolean functions, then the number of solutions of an equation $F(x) = A$ is even. Finally, we describe a new class of proper families of Boolean functions.
Keywords: proper family of Boolean functions, triangular family. 
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     author = {K. D. Tsaregorodtsev},
     title = {Properties of proper families of {Boolean} functions},
     journal = {Diskretnaya Matematika},
     pages = {91--102},
     publisher = {mathdoc},
     volume = {33},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2021_33_1_a7/}
}
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K. D. Tsaregorodtsev. Properties of proper families of Boolean functions. Diskretnaya Matematika, Tome 33 (2021) no. 1, pp. 91-102. http://geodesic.mathdoc.fr/item/DM_2021_33_1_a7/