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On Crown-Free Set Families, Diffusion State Difference, And Non-Uniform Hypergraphs, Edward Lawrence Boehnlein

Theses and Dissertations

We present results in three different arenas of discrete mathematics. Let La(n, H) denote the cardinality of the largest family on the Boolean lattice that does not contain H as a subposet. Denote π(H) := limn→∞ La(n,H) (bn/ n2c) . A crown O2k for k ≥ 2 is a poset on 2 levels whose Hasse diagram is a cycle. Griggs and Lu (2009) showed π(O4k) = 1 for k ≥ 2. Lu (2014) proved π(O2k) = 1 for odd k ≥ 7. We prove that the maximum size of a O6 -free family, when restricted to the middle two levels …