Abstract
In the middle 1930's, the early days of combinatorial lattice theory, it had been conjectured thatin any finite modular lattice the number of join-irreducible elements equals the number of meetirreducible elements. The conjecture was settled in 1954 by R. P. Dilworth in a remarkable combinatorial generalization. Quite recently we have been led to this question. Which ordered setsS satisfy the property that,for any modular lattice M, the number of subdiagrams of M isomorphic to S equals the number of subdiagrams of M dually isomorphic to S?
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