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Diagonals of Doubly Stochastic Matrices

Published online by Cambridge University Press:  20 November 2018

George Maxwell
George Maxwell*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Let A be an additive abelian group and Dn(A) the set of those n x n matrices over A all of whose row and column sums are equal. Such matrices can be regarded as a possible generalization of doubly stochastic real matrices; alternatively, if A is a commutative ring, it turns out that Dn(A) is exactly the image of the permutation representation of Sn, the symmetric group of degree n, over A.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 239 - 241
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Wang, E. T. H., The diagonal sums of doubly stochastic matrices, (to appear).Google Scholar
2. Marcus, M. and Mine, H., Some results on doubly stochastic matrices, Proc. Amer. Math. Soc. 13 (1962), 571-579.Google Scholar