Abstract
The absolute upper shadow of a family A of r-sets on {1, ..., n} is \(bar \partial \) A = {A ∪ {i} : A ∈ A, i ∉ A, i ∈ ∪ A}. Given |A|, how small can \(bar \partial \) A be? Our aim in this note is to give an exact solution to this question. Curiously, the extremal sets turn out not to form a nested nestedfamily.
Our main tool is an inequality concerning the colex ordering that may be of independent interest.
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© 2000 Springer Science+Business Media New York
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Bollobás, B., Leader, I. (2000). Minimizing the Absolute Upper Shadow. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_7
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DOI: https://doi.org/10.1007/978-1-4757-6048-4_7
Publisher Name: Springer, Boston, MA
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