  Entanglement catalysis allows one to convert certain entangled states into
others by the temporary involvement of another entangled state (so-called
catalyst), where after the conversion the catalyst is returned to the same
state. For bipartite pure entangled states that can be transformed in this way
with unit probability, the respective Schmidt coefficients are said to satisfy
the trumping relation, a mathematical relation which is an extension of the
majorization relation. This article provides all necessary and sufficient
conditions for the trumping relation in terms of the Schmidt coefficients. The
coefficients should satisfy strict inequalities for the entropy of entanglement
and for power means excluding the special power 1.
