Geodesic
Diagonals of Doubly Stochastic Matrices
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 239-241

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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. 
Maxwell, George. Diagonals of Doubly Stochastic Matrices. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 239-241. doi: 10.4153/CMB-1972-044-7
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     title = {Diagonals of {Doubly} {Stochastic} {Matrices}},
     journal = {Canadian mathematical bulletin},
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     year = {1972},
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     number = {2},
     doi = {10.4153/CMB-1972-044-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-044-7/}
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