The number of finite distributive lattices
by
Jürgen Reinhold
Universität Hannover
Coauthors: Jobst Heitzig, Marcel Erné

Let d(n) denote the number of isomorphism classes of distributive lattices with n elements. Using an orderly algorithm implemented on a CRAY T3e, we have computed the numbers d(n) up to n=49. We did not succeed in finding an asymptotic formula for the numbers d(n), but we are able to prove bounds like 1.8ⁿ <= d(n) <= 4ⁿ.
The main subject of the talk will be to present an algorithm which yields for every isomorphism class of distributive lattices with n elements and height h a sequence a₁ <= a₂ <= ... <= a_h with a_i in { 1, ..., n} which 'codes' the isomorphism class, i.e. the isomorphism class can again easily be deduced from this sequence. Since h <= n, this proves the upper bound d(n) <= 4ⁿ.

Date received: May 23, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caee-61.