  The classic method for mass determination in a SUSY-like cascade decay chain
relies on measurements of the kinematic endpoints in the invariant mass
distributions of suitable collections of visible decay products. However, the
procedure is complicated by combinatorial ambiguities: e.g., the visible final
state particles may be indistinguishable (as in the case of QCD jets), or one
may not know the exact order in which they are emitted along the decay chain.
In order to avoid such combinatorial ambiguities, we propose to treat the final
state particles fully democratically and consider the sorted set of the
invariant masses of all possible partitions of the visible particles in the
decay chain. In particular, for a decay to N visible particles, one considers
the sorted sets of all possible n-body invariant mass combinations (2 <= n <=
N) and determines the kinematic endpoint m_(n,r)^max of the distribution of the
r-th largest n-body invariant mass m_(n,r) for each possible value of n and r.
For the classic example of a squark decay in supersymmetry, we provide
analytical formulas for the interpretation of these endpoints in terms of the
underlying physical masses. We point out that these measurements can be used to
determine the structure of the decay topology, e.g., the number and position of
intermediate on-shell resonances.
