This article is cited in 2 papers

On the perfectness of minimal regular partitions of the edge set of the $n$-dimensional cube

K. L. Rychkov

Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia

Abstract: 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.

UDC: 519.714

Received: 10.06.2019
Revised: 29.07.2019
Accepted: 28.08.2019

DOI: 10.33048/daio.2019.26.662