Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order
Jonathan David Farley · Canadian Mathematical Bulletin · 2011
Abstract Let L be a finite distributive lattice. Let Sub0(L) be the lattice ﹛S | S is a sublattice of L﹜ [ ﹛∅﹜ and let ℓ*[Sub0(L)] be the length of the shortest maximal chain in Sub0(L). It is proved that if K and L are non-trivial finite distributive lattices, then ℓ*[Sub0(K × L)] = ℓ*[Sub0(K)] + ℓ[Sub0(L)]. A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved.