Abstract
For a finite lattice L, denote by l ∗(L) and l ∗(L) respectively the upper length and lower length of L. The grading number g( L) of L is defined as g(L) = l ∗( Sub(L))-l ∗( Sub(L)) where Sub( L) is the sublattice-lattice of L. We show that if K is a proper homomorphic image of a distributive lattice L, then l ∗( Sub(K)) < l ∗( Sub(L)) ; and derive from this result, formulae for l ∗( Sub(L)) and g( L) where L is a product of chains.
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