On the volume of the polytope of doubly stochastic matrices
| dc.creator | Chan, Clara S. | |
| dc.creator | Robbins, David P. | |
| dc.date | 1998-06-13 | |
| dc.date.accessioned | 2026-07-07T05:25:02Z | |
| dc.date.available | 2026-07-07T05:25:02Z | |
| dc.description | We study the calculation of the volume of the polytope B_n of n by n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a decomposition of the polytope into simplices. The second involves the enumeration of ``magic squares'', i.e., n by n non-negative 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 B_n. For example, we have observed that the volume of a particular face of B_n 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. | |
| dc.identifier | https://arxiv.org/abs/math/9806076 | |
| dc.identifier | http://arxiv.org/abs/math/9806076 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77040 | |
| dc.subject | Combinatorics | |
| dc.title | On the volume of the polytope of doubly stochastic matrices | |
| dc.type | text |