Maximal Sublattices of Finite Distributive Lattices. III: A Conjecture from the 1984 Banff Conference on Graphs and Order
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Published:2011-06-01
Issue:2
Volume:54
Page:277-282
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. math. bull.
Author:
Farley Jonathan David
Abstract
AbstractLet L be a finite distributive lattice. Let Sub0(L) be the lattice﹛S | S is a sublattice of L﹜ [ ﹛∅﹜
and let ℓ*[Sub0(L)] be the length of the shortest maximal chain in Sub0(L). It is proved that if K and L are non-trivial finite distributive lattices, then
ℓ*[Sub0(K × L)] = ℓ*[Sub0(K)] + ℓ[Sub0(L)].
A conjecture from the 1984 Banff Conference on Graphs and Order is thus proved.
Publisher
Canadian Mathematical Society
Subject
General Mathematics