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A few years ago, in a short paper (4) Ryser introduced an interesting topic in number theory, viz. the connection between integer matrices (i.e., matrices having only integers as their elements) satisfying certain conditions and 0-1 matrices (i.e., matrices that have no element different from 0 and 1). In this series of papers we shall pursue this topic further.
To make the statements of our theorems short we introduce some terminology. We need the definitions of certain 0-1 matrices related to a few well-known combinatorial configurations. By an incidence matrix of a balanced incomplete block (b.i.b. for conciseness) design we mean a 0-1 matrix with v rows and b columns, such that the sum of the elements in each column of A is k, k < v, and the scalar product of any two row vectors of A is λ, λ ≠ 0.