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Summary: Q2-free families in the Boolean lattice
Maria Axenovich
Iowa State University
Ames, IA 50010
axenovic@iastate.edu
Jacob Manske
Iowa State University
Ames, IA 50010
jmanske@iastate.edu
Ryan Martin
Iowa State University
Ames, IA 50010
rymartin@iastate.edu
December 23, 2009
Abstract
For a family F of subsets of [n] = {1, 2, . . . , n} ordered by inclusion, and a partially ordered set P, we
say that F is P-free if it does not contain a subposet isomorphic to P. Let ex(n, P) be the largest size
of a P-free family of subsets of [n]. Let Q2 be the poset with distinct elements a, b, c, d, a < b, c < d; i.e.,
the 2-dimensional Boolean lattice. We show that 2N - o(N) ex(n, Q2) 2.283261N + o(N), where
N =
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