Geodesic
Minimal in terms of double-sided shadow subsets of Boolean cube layer distinct from circles
Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 5, pp. 3-20.

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The double-shadow minimization problem in the Boolean cube layer is considered. The final lexicographical segment of the second layer is shown to have the minimal double-sided shadow. The minimal families of size $1+k(n-k)+(k-1)(n-k-1)$ in the $k$th layer are described when $n=2k$ for small values of $k$. Bibliogr. 5.
Keywords: shadow minimization, double-sided shadow, Boolean cube, ideal weight minimization. 
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M. A. Bashov. Minimal in terms of double-sided shadow subsets of Boolean cube layer distinct from circles. Diskretnyj analiz i issledovanie operacij, Tome 19 (2012) no. 5, pp. 3-20. http://geodesic.mathdoc.fr/item/DA_2012_19_5_a0/

[1] Bashov M. A., “Minimizatsiya dvustoronnei teni v edinichnom kube”, Diskret. matematika, 23:4 (2011), 115–132 | DOI | MR

[2] Ahlswede R., Aydinian H., Khachatrian L. H., “More about shifting techniques”, Eur. J. Comb., 24 (2003), 551–556 | DOI | MR | Zbl

[3] Clements G. F., Lindström B., “A generalization of a combinatorial theorem of Macaulay”, J. Comb. Theory, 7 (1969), 230–238 | DOI | MR | Zbl

[4] Katona G. O. H., “A theorem of finite sets”, Proc. Tihany Conf., Academic Press, New York, 1966, 187–207 | MR

[5] Kruskal J., “The number of simplices in a complex”, Mathematical optimization techniques, Univ. California Press, Berkeley–Los Angeles, 1963, 251–278 | MR