Geodesic
Sunflowers in lattices
The electronic journal of combinatorics, Tome 12 (2005)
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A Sunflower is a subset $S$ of a lattice, with the property that the meet of any two elements in $S$ coincides with the meet of all of $S$. The Sunflower Lemma of Erdös and Rado asserts that a set of size at least $1 + k!(t-1)^k$ of elements of rank $k$ in a Boolean Lattice contains a sunflower of size $t$. We develop counterparts of the Sunflower Lemma for distributive lattices, graphic matroids, and matroids representable over a fixed finite field. We also show that there is no counterpart for arbitrary matroids.
DOI : 10.37236/1963
Classification : 05B35, 06A07
Mots-clés : sunflower lemma, lattice, geometric lattice, distributive lattice, matroid 
@article{10_37236_1963,
     author = {Geoffrey McKenna},
     title = {Sunflowers in lattices},
     journal = {The electronic journal of combinatorics},
     year = {2005},
     volume = {12},
     doi = {10.37236/1963},
     zbl = {1123.05026},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1963/}
}
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Geoffrey McKenna. Sunflowers in lattices. The electronic journal of combinatorics, Tome 12 (2005). doi: 10.37236/1963

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