On the variation of co-ordinates in subspaces

Summary Let1≦k≦n−1, 2≦n. This paper examines the vectors δ_p(L_k), where L_k is a k-dimensional subspace of an n-dimensional space, and the co-ordinates of δ_p(L_k) are given below by (1.1). For fixed k, the set of such vectors as L_k varies is determined for p=2. For general p, information is given on upper and lower bounds for the sum of the co-ordinates of δ_p(L_k). Dedicated to the sixtieth birthday of Prof. Edgar R. Lorch This research was supported in part by the Office of Naval Research under contract number Nonr 3775(09), NR 047040.