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A problem on 0-1 matrices. (English) Zbl 0741.15007
Author’s summary: We compute the maximal and the minimal value of \(\| M^ 2\|\) over the class of \(0-1\) valued \(n\times n\) matrices \(M\) with \(k\) entries equal to one for fixed \(k\) and \(n\), where \(\|\centerdot\|\) denotes the sum of the entries. This result has applications to graph theory and probability theory.

15B36 Matrices of integers
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
60G10 Stationary stochastic processes
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
0–1 matrices; norm
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