Boolean algebras and Lubell functions

@article{Johnston2015BooleanAA,
  title={Boolean algebras and Lubell functions},
  author={J. Travis Johnston and Linyuan Lu and Kevin G. Milans},
  journal={J. Comb. Theory, Ser. A},
  year={2015},
  volume={136},
  pages={174-183}
}
Let 2 denote the power set of [n], where [n] = {1, 2, . . . , n}. A collection B ⊂ 2 forms a d-dimensional Boolean algebra if there exist pairwise disjoint sets X0, X1, . . . , Xd ⊆ [n], all non-empty with perhaps the exception of X0, so that B = { X0 ∪ ⋃ i∈I Xi : I ⊆ [d] } . Let b(n, d) be the maximum cardinality of a family F ⊂ 2 that does not contain a d-dimensional Boolean algebra. Gunderson, Rödl, and Sidorenko proved that b(n, d) ≤ cdn d · 2 where cd = 10d2−2 1−d dd−2 −d . In this paper… CONTINUE READING

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