Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4655136 | Journal of Combinatorial Theory, Series A | 2015 | 17 Pages |
Abstract
Let F be a family of subsets of {1,â¦,n}. We say that F is P-free if the inclusion order on F does not contain P as an induced subposet. The Turán function of P, denoted Laâ(n,P), is the maximum size of a P-free family of subsets of {1,â¦,n}. We show that Laâ(n,P)â¤(4r+O(r))(nân/2â) if P is an r-element poset of height at most 2. We also show that Laâ(n,Sr)=(r+O(r))(nân/2â) where Sr is the standard example on 2r elements, and that Laâ(n,2[2])â¤(2.583+o(1))(nân/2â), where 2[2] is the 2-dimensional Boolean lattice.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Linyuan Lu, Kevin G. Milans,