Geodesic
On the perfectness of minimal regular partitions of the edge set of the $n$-dimensional cube
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 4, pp. 74-107

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We prove that, for $n$ equal to $3$, $5$, and a power of $2$, every minimal partition of the edge set of the $n$-dimensional cube is perfect. As a consequence, we obtain some description of the classes of all minimal parallel-serial contact schemes ($\pi$-schemes) realizing the linear Boolean functions that depend essentially on $n$ variables for the corresponding values of $n$. Bibliogr. 16.
Keywords: Boolean function, $\pi$-scheme, regular partition of the edge set of the $n$-dimensional cube, lower complexity bound. 
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     author = {K. L. Rychkov},
     title = {On the perfectness of minimal regular partitions of the edge set of the $n$-dimensional cube},
     journal = {Diskretnyj analiz i issledovanie operacij},
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K. L. Rychkov. On the perfectness of minimal regular partitions of the edge set of the $n$-dimensional cube. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 4, pp. 74-107. http://geodesic.mathdoc.fr/item/DA_2019_26_4_a4/