Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


An inductive algorithm to construct finite lattices

Author: Shoji Kyuno
Journal: Math. Comp. 33 (1979), 409-421
MSC: Primary 06B05
MathSciNet review: 514837
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: G. Birkhoff [1] proposed the following problem: Enumerate all finite lattices which are uniquely determined (up to isomorphism) by their diagram, considered as a graph.

It is not known how many lattices of order n exist, except when the value of n is quite small. The aim of this note is to give an algorithm to construct inductively all finite lattices of order n. Using this algorithm, we have found that there exist 222 lattices for $ n = 8$ and 1078 lattices for $ n = 9$. All lattices of order $ n \leqslant 8$ are shown at the end of this note.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 06B05

Retrieve articles in all journals with MSC: 06B05

Additional Information

PII: S 0025-5718(1979)0514837-9
Article copyright: © Copyright 1979 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia