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. 
@article{DA_2012_19_5_a0,
     author = {M. A. Bashov},
     title = {Minimal in terms of double-sided shadow subsets of {Boolean} cube layer distinct from circles},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {3--20},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2012_19_5_a0/}
}
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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/