## On the shadow of squashed families of $$k$$-sets.(English)Zbl 0824.05003

Electron. J. Comb. 2, Research paper R16, 6 p. (1995); printed version J. Comb. 2, 263-270 (1995).
Summary: The shadow of a collection $$\mathcal A$$ of $$k$$-sets is defined as the collection of the $$(k- 1)$$-sets which are contained in at least one $$k$$- set of $$\mathcal A$$. Given $$| {\mathcal A}|$$, the size of the shadow is minimum when $$\mathcal A$$ is the family of the first $$k$$-sets in squashed order (by definition, a $$k$$-set $$A$$ is smaller than a $$k$$-set $$B$$ in the squashed order if the largest element of the symmetric difference of $$A$$ and $$B$$ is in $$B$$). We give a tight upper bound and an asymptotic formula for the size of the shadow of squashed families of $$k$$-sets.

### MSC:

 05A16 Asymptotic enumeration
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