Name
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. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.jcta.2012.11.002 | J. Comb. Theory, Ser. A |
Keywords | Field | DocType |
distinct element,elements b,empty set,following property,n-dimensional boolean lattice,diamond-free subposets,boolean lattice,so-called lubell function,diamond-free family | Diamond,Discrete mathematics,Empty set,Combinatorics,Boolean algebra (structure),Mathematics | Journal |
Volume | Issue | ISSN |
120 | 3 | 0097-3165 |
Citations | PageRank | References |
15 | 0.89 | 8 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lucas Kramer | 1 | 15 | 1.57 |
| Ryan R. Martin | 2 | 36 | 10.12 |
| Michael Young | 3 | 49 | 5.07 |