Nonexistence of a Kruskal–Katona type theorem for double-sided shadow minimization in the Boolean cube layer
| 30 mai 2014
À propos de cet article
Publié en ligne: 30 mai 2014
Pages: 53 - 62
Reçu: 05 févr. 2013
DOI: https://doi.org/10.2478/ausi-2014-0004
© 2014
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A double-sided shadow minimization problem in the Boolean cube layer is investigated in this paper. The problem is to minimize the size of the union of the lower and upper shadows of a k-uniform family of subsets of [n]. It is shown that if 3 ⋜ k ⋜ n−3, there is no total order such that all its initial segments have minimal double-sided shadow.