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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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An inductive algorithm to construct finite lattices
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by Shoji Kyuno PDF
Math. Comp. 33 (1979), 409-421 Request permission


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.
  • Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 409-421
  • MSC: Primary 06B05
  • DOI:
  • MathSciNet review: 514837