An inductive algorithm to construct finite lattices

Author:
Shoji Kyuno

Journal:
Math. Comp. **33** (1979), 409-421

MSC:
Primary 06B05

MathSciNet review:
514837

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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 and 1078 lattices for . All lattices of order are shown at the end of this note.

**[1]**Garrett Birkhoff,*Lattice theory*, Third edition. American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR**0227053**

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0514837-9

Article copyright:
© Copyright 1979
American Mathematical Society