The asymptotic volume of the Birkhoff polytope
| dc.creator | Canfield, E. Rodney | |
| dc.creator | McKay, Brendan D. | |
| dc.date | 2007-05-16 | |
| dc.date.accessioned | 2026-07-07T08:02:28Z | |
| dc.date.available | 2026-07-07T08:02:28Z | |
| dc.description | Let m,n be positive integers. Define T(m,n) to be the transportation polytope consisting of the m x n non-negative real matrices whose rows each sum to 1 and whose columns each sum to m/n. The special case B(n)=T(n,n) is the much-studied Birkhoff-von Neumann polytope of doubly-stochastic matrices. Using a recent asymptotic enumeration of non-negative integer matrices (Canfield and McKay, 2007), we determine the asymptotic volume of T(m,n) as n goes to infinity, with m=m(n) such that m/n neither decreases nor increases too quickly. In particular, we give an asymptotic formula for the volume of B(n). | |
| dc.description | 4 pages, 1 table | |
| dc.identifier | https://arxiv.org/abs/0705.2422 | |
| dc.identifier | http://arxiv.org/abs/0705.2422 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/129239 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A16; 52B05 | |
| dc.title | The asymptotic volume of the Birkhoff polytope | |
| dc.type | text |