Geodesic
On the shadow of squashed families of \(k\)-sets
The electronic journal of combinatorics, Tome 2 (1995)
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The shadow of a collection ${\cal A}$ of $k$-sets is defined as the collection of the $(k-1)$-sets which are contained in at least one $k$-set of ${\cal A}$. Given $|{\cal A}|$, the size of the shadow is minimum when ${\cal A}$ 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.
DOI : 10.37236/1210
Classification : 05A16
Mots-clés : shadow, squashed order, symmetric difference, upper bound, asymptotic formula, size of the shadow, squashed families of \(k\)-sets 
@article{10_37236_1210,
     author = {Fr\'ed\'eric Maire},
     title = {On the shadow of squashed families of \(k\)-sets},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1210},
     zbl = {0824.05003},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1210/}
}
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%J The electronic journal of combinatorics
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Frédéric Maire. On the shadow of squashed families of \(k\)-sets. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1210

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