Proof of a Conjecture on Finite Modular Lattices
R. P. Dilworth · Birkhäuser Boston eBooks · 1990
Since the middle 1930’s when the work of Birkhoff and Ore stimulated the modern development of lattice theory, it has been conjectured that in a finite modular lattice the number of meet irreducibles is equal to the number of join irreducibles. 1 I shall prove here the following general combinatorial theorem on finite modular lattices which includes a proof of this conjecture as a special case.