The following conjecture of U Faigle and B Sands is proved: For every number R > 0 there exists a number n(R) such that if L is a finite distributive lattice whose width w(L) (size of the largest antichain) is at least n(R), then |L| ≥ Rw(L). In words this says that as one considers increasingly large distributive lattices, the maximum sized antichain contains a vanishingly small proportion of the elements.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics