On Rota′s Problem About n Bases in a Rank n Matroid

The N-Membranes Problem

The number of rank-k flats in a matroid with no U2, n-minor

We show that, if k and ` are positive integers and r is sufficiently large, then the number of rank-k flats in a rank-r matroid M with no U2,`+2-minor is less than or equal to number of rank-k flats in a rank-r projective geometry over GF(q), where q is the largest prime power not exceeding `.

(n,1,1,α)-Center Problem

Given a set  of  points in the plane and a constant ,-center problem is to find two closed disks which each covers the whole , the diameter of the bigger one is minimized, and the distance of the two centers is at least . Constrained -center problem is the -center problem in which the centers are forced to lie on a given line . In this paper, we first introduce -center problem and its constrain...

On the rank of $n\times n$ matrix multiplication

For every p 6 n positive integer we obtain the lower bound (3 − 1 p+1 )n −

the n-membranes problem