Distributive lattices determined by weighted double skeletons
  Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive lattice and its second skeleton, S(S(D)), is the trivial lattice, then D is characterized by its weighted double skeleton, introduced by the second author in 2006. The assumption on the second skeleton is essential. 
G\'abor Cz\'edli, Joanna Grygiel, Katarzyna Grygiel
math.RA