International Journal of Mathematics and Mathematical Sciences
Volume 6 (1983), Issue 3, Pages 409-418
Dot product rearrangements
Mathematics Institute, University of Cincinnati, Budapest, Hungary
Received 18 September 1980
Copyright © 1983 Paul Erdos and Gary Weiss. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let , denote nonnegative sequences; denotes the rearranged sequence determined by the permutation , denotes the dot product ; and denotes . We examine as a subset of the nonnegative real line in certain special circumstances. The main result is that if , then for every if and only if is uniformly bounded.