Mar 26, 2008 · We asymptotically determine the size of the largest family F of subsets of {1,...,n} not containing a given poset P if the Hasse diagram of P is a tree.

Nov 30, 2009 · Abstract. We asymptotically determine the size of the largest family F F of subsets of {1,…,n} { 1 , … , n } not containing a given poset P ...

Definition. Set family is a collection of subsets of [n]. In symbols, F ⊂ 2[n]. Theorem (Sperner'28). Suppose F ⊂ 2[n] ...

We say that a poset P is a subposet of a poset P′ if there is an injective map f : P → P′ such that a ≤P b implies f(a) ≤P ′ f(b).

In this paper we exa mine the size of the largest family F ⊂ 2 [ n ] subject to the condition that F does not contain a fixed finite subposet P.

A poset P is a subposet of Q if P ⊆ Q and x ≤ P y if and only if x ≤ Q y . We say that Q contains a copy of P if P is a subposet of Q. If P and Q have the ...

Generally speaking, induced subposets are harder to force, since we need to enforce non-containment as well as containment among corresponding members. For.

Let $F$ be a family of subsets of $\{1,\ldots,n\}$. We say that $F$ is $P$-free if the inclusion order on $F$ does not contain $P$ as an induced subposet.

Jun 7, 2015 · We seek the largest set families whose inclusion order does not contain a copy of a fixed poset. A poset P is a subposet of Q if P ⊆ Q and x ≤P ...

Theorem (Sperner 1928). Let F be a family of subsets of [n] = {1,2,...,n}. Suppose. “For any A, B ∈ F, neither A ⊂ B nor B ⊂ A.”.