  We introduce the honeycomb model of BZ polytopes, which calculate
Littlewood-Richardson coefficients, the tensor product rule for GL(n). Our main
result is the existence of a particularly well-behaved honeycomb with given
boundary conditions (choice of triple of representations to be tensored
together). This honeycomb is necessarily integral, which proves the "saturation
conjecture", extending results of Klyachko to give a complete answer to which
L-R coefficients are positive. This in turn has as a consequence Horn's
conjecture from 1962 characterizing the spectrum of the sum of two Hermitian
matrices.
