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.Comment: 12 pages and 2 figure
