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

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

Journal

Journal of Applied and Industrial Mathematics
ISSN: 1990-4789 , E-ISSN: 1990-4797

Output data

Year: 2019, Volume: 13, Number: 4, Pages: 717-739 Pages count : 23 DOI: 10.1134/S1990478919040148

Tags

Boolean function, π-scheme, regular partition of the edge set of the n-dimensional cube, lower complexity bound

Authors

Rychkov Konstantin Leonidovich ¹

Affiliations

1	Sobolev Institute of Mathematics

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 (π-schemes) realizing the linear Boolean functions that depend essentially on n variables for the corresponding values of n.

Rychkov K.L.
On the perfectness of minimal regular partitions of the edge set of the n-dimensional cube
Journal of Applied and Industrial Mathematics. 2019. V.13. N4. P.717-739. DOI: 10.1134/S1990478919040148 Scopus OpenAlex

Рычков К.Л.
О совершенности минимальных правильных разбиений множества ребер n-мерного куба
Дискретный анализ и исследование операций. 2019. Т.26. №4. С.74-107. DOI: 10.33048/daio.2019.26.662 OpenAlex

Scopus:	2-s2.0-85078933769
OpenAlex:	W2999099985

DB	Citing
Scopus	2