  We conjecture a new set of analytic relations for scattering amplitudes in
planar N=4 super Yang-Mills theory. They generalise the Steinmann relations and
are expressed in terms of the cluster algebras associated to Gr(4,n). In terms
of the symbol, they dictate which letters can appear consecutively. We study
heptagon amplitudes and integrals in detail and present symbols for previously
unknown integrals at two and three loops which support our conjecture.
