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...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

For a representation of a matroid the combinatorially defined Kazhdan-Lusztig polynomial computes the intersection cohomology of the associated reciprocal plane. However, these polynomials are difficult to compute and there are numerous open conjectures about their structure. For example, it is unknown whether or not the coefficients are non-negative for non-representable matroids. The main res...