The Ehrhart polynomial of the Birkhoff polytope
Matthias Beck and Dennis Pixton

n = 10

The calculation of the volume of the Birkhoff polytope when n = 10 requires the evaluation of 4862 integrals. We started the calculation on March 13, 2002, using between 10 and 40 computers (depending on load).

The last integral was finished on May 18, 2003 The total computer time, scaled to a "standard" processor running at 1 GHz, is

6160 days, or almost 17 years.

And here's the answer:

727291284016786420977508457990121862548823260052557333386607889 / 828160860106766855125676318796872729344622463533089422677980721388055739956270293750883504892820848640000000