Whitney Number Inequalities for Geometric Lattices
نویسندگان
چکیده
Let L be a finite geometric lattice of rank r, and for i =0, I, •• •» r, let W. denote the number of elements of L with rank i. F or 1 < k < r 2, we have W, + W. + • • • + V, < W ,+•••+ W ., + W , 12 fe r—k r—l r—1 with equality if and only if the lattice L is modular. We give two further results concerning matchings of lattice elements of rank < k into those of rank > r — k, and observe that a middle term can be interpolated in the above inequality.
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