Matrices with prescribed row, column and block sums

Abstract

The main result of the paper is Theorem 1. It concerns the sets of integral symmetric matrices with given block partition and prescribed row, column and block sums. It is shown that by interchanges preserving these sums we can pass from any two matrices, one from each set, to the other two ones falling “close” together as much as possible. One of the direct corollaries of Theorem 1 is substantiating the fact that any realization ofr-graphical integer-pair sequence can be obtained from any other one byr-switchings preserving edge degrees. This result is also of interest in connection with the problem of determinings-complete properties. In the special cases Theorem 1 includes a number of well-known results, some of which are presented.

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Chernyak, Z.A., Chernyak, A.A. Matrices with prescribed row, column and block sums. Combinatorica 8, 177–184 (1988). https://doi.org/10.1007/BF02122798

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AMS subject classifications (1980)

  • 05 B 20
  • 05 C 99