The volume of the 10th Birkhoff polytope
| dc.creator | Beck, Matthias | |
| dc.creator | Pixton, Dennis | |
| dc.date | 2003-05-23 | |
| dc.date.accessioned | 2026-07-07T04:58:13Z | |
| dc.date.available | 2026-07-07T04:58:13Z | |
| dc.description | The n'th Birkhoff polytope $B_n$ is the set of all doubly stochastic $n \times n$ matrices, that is, those matrices with nonnegative real coefficients in which every row and column sums to one. A long-standing open problem is the determination of the relative volume of $B_n$. In [arXiv:math.CO/0202267] we introduced a method of calculating this volume and used it to compute $\vol B_9$. This note is an update on our progress: with the same program (but much longer computing time), we have now derived $\vol B_{10}$. | |
| dc.description | 1 page, not to be published elsewhere | |
| dc.identifier | https://arxiv.org/abs/math/0305332 | |
| dc.identifier | http://arxiv.org/abs/math/0305332 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67547 | |
| dc.subject | Combinatorics | |
| dc.subject | 52B20; 05A15, 52C07 | |
| dc.title | The volume of the 10th Birkhoff polytope | |
| dc.type | text |