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Crowns, Fences, and Dismantlable Lattices

Published online by Cambridge University Press:  20 November 2018

David Kelly  and
Ivan Rival
David Kelly
Affiliation:
University of Manitoba, Winnipeg, Manitoba
Ivan Rival
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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A finite lattice L of order n is dismantlable [6] if there is a chain L1 ⊂ L2 ⊂ . . . ⊂ Ln = L of sublattices of L such that |Li| = i for every i = 1, 2, . . . , n. In [1] it was shown that every finite planar lattice is dismantlable. Furthermore, every lattice L with |L| ≦ 7 is dismantlable [6]; in fact, every large enough lattice contains a dismantlable sublattice with precisely n elements [4]. As well, such lattices are closed under the formation of sublattices and homomorphic images [6].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1257 - 1271
Copyright
Copyright © Canadian Mathematical Society 1974

References

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