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- W2591983047 abstract "We study the calculation of the volume of the polytope Bn of n × n doubly stochastic matrices (real nonnegative matrices with row and column sums equal to one). We describe two methods. The first involves a decompos ition of the polytope into simplices. The second involves the enumeration of “magic squares”, that is, n × n nonnegative integer matrices whose rows and columns all sum to the same integer. We have used the first method to confirm the previously known values through n = 7. This method can also be used to compute the volumes of faces of Bn For example, we have observed that the volume of a particular face of Bn appears to be a product of Catalan numbers. We have used the second method to find the volume for n = 8, which we believe was not previously known." @default.
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- W2591983047 date "1999-01-01" @default.
- W2591983047 modified "2023-09-25" @default.
- W2591983047 title "On the Volume of the Polytope of Doubly Stochastic Matrices" @default.
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- W2591983047 doi "https://doi.org/10.1080/10586458.1999.10504406" @default.
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