Abstract
Let ℬ(m) be the set of all then-square (0–1) matrices containingm ones andn 2−m zeros, 0<m<n 2. The problem of finding the maximum ofs(A 2) over this set, wheres(A 2) is the sum of the entries ofA 2,A ∈ ℬ (m) is considered. This problem is solved in the particular casesm=n 2 −k 2 andm=k 2,k 2>(n 2/2).
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This paper forms part of a thesis in partial fulfillment of the requirements for the degree of Doctor of Science at the Technion-Israel Institute of Technology. The author wishes to thank Professor B. Schwarz and Dr. D. London for their help in the preparation of this paper.
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Katz, M. Rearrangements of (0–1) matrices. Israel J. Math. 9, 53–72 (1971). https://doi.org/10.1007/BF02771620
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DOI: https://doi.org/10.1007/BF02771620