On the Number of Distributive Lattices

We investigate the numbers dk of all (isomorphism classes of) distributive lattices with k elements, or, equivalently, of (unlabeled) posets with k antichains. Closely related and useful for combinatorial identities and inequalities are the numbers vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the following exponential bounds:

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Marcel Erné, Jobst Heitzig, Jürgen Reinhold
• Keywords: COMBINATORICS 2002, Distributive Lattices, Indecomposable Distributive Lattices, Isomorphism Classes