Email this article On the Perfectness of Minimal Regular Partitions of the Edge Set of the n-Dimensional Cube
- Authors: Rychkov K.L.1
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Affiliations:
- Sobolev Institute of Mathematics
- Issue: Vol 13, No 4 (2019)
- Pages: 717-739
- Section: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213287
- DOI: https://doi.org/10.1134/S1990478919040148
- ID: 213287
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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 (π-schemes) realizing the linear Boolean functions that depend essentially on n variables for the corresponding values of n.
About the authors
K. L. Rychkov
Sobolev Institute of Mathematics
Author for correspondence.
Email: rychkov@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090
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