Abstract
The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: A⊂B,C⊂D. A diamond-free family in the n-dimensional Boolean lattice is a subposet such that no four elements form a diamond. Note that elements B and C may or may not be related.There is a diamond-free family in the n-dimensional Boolean lattice of size (2−o(1))(n⌊n/2⌋). In this paper, we prove that any diamond-free family in the n-dimensional Boolean lattice has size at most (2.25+o(1))(n⌊n/2⌋). Furthermore, we show that the so-called Lubell function of a diamond-free family in the n-dimensional Boolean lattice which contains the empty set is at most 2.25+o(1), which is asymptotically best possible.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
