2 results
Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order
-
- Journal:
- Canadian Mathematical Bulletin / Volume 54 / Issue 2 / 01 June 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 277-282
- Print publication:
- 01 June 2011
-
- Article
-
- You have access
- Export citation
-
Let
$L$ be a finite distributive lattice. Let 
$\text{Su}{{\text{b}}_{0}}(L)$ be the lattice
$$\{S\,|\,S\,\text{is}\,\text{a sublattice of }L\}\cup \{\phi \}$$and let
${{\ell }_{*}}[\text{Su}{{\text{b}}_{0}}(L)]$ be the length of the shortest maximal chain in $\text{Su}{{\text{b}}_{0}}(L)$. It is proved that if 
$K$ and $L$ are non-trivial finite distributive lattices, then
$${{\ell }_{*}}[\text{Su}{{\text{b}}_{0}}(K\times L)]={{\ell }_{*}}[\text{Su}{{\text{b}}_{0}}(K)]+{{\ell }_{*}}[\text{Su}{{\text{b}}_{0}}(L)]$$A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved.
Covering in the lattice of subuniverses of a finite distributive lattice
- Part of
-
- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 65 / Issue 3 / December 1998
- Published online by Cambridge University Press:
- 09 April 2009, pp. 333-353
- Print publication:
- December 1998
-
- Article
-
- You have access
- Export citation
