Geodesic
Flattening antichains with respect to the volume
The electronic journal of combinatorics, Tome 6 (1999)
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We say that an antichain $\cal A$ in the boolean lattice $B_n$ is flat if there exists an integer $k\geq 0$ such that every set in $\cal A$ has cardinality either $k$ or $k+1$. Define the volume of $\cal A$ to be $\sum_{A\in{\cal A}}|A|$. We prove that for every antichain $\cal A$ in $B_n$ there exist an antichain which is flat and has the same volume as $\cal A$.
DOI : 10.37236/1433
Classification : 05D99, 06A07, 06E99
Mots-clés : poset, volume, flat, antichain 
@article{10_37236_1433,
     author = {Ljiljana Brankovic and Paulette Lieby and Mirka Miller},
     title = {Flattening antichains with respect to the volume},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1433},
     zbl = {0913.05092},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1433/}
}
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Ljiljana Brankovic; Paulette Lieby; Mirka Miller. Flattening antichains with respect to the volume. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1433

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