  Seriation methods order a set of descriptions given some criterion (e.g.,
unimodality or minimum distance between similarity scores). Seriation is thus
inherently a problem of finding the optimal solution among a set of
permutations of objects. In this short technical note, we review the
combinatorial structure of the classical seriation problem, which seeks a
single solution out of a set of objects. We then extend those results to the
iterative frequency seriation approach introduced by Lipo (1997), which finds
optimal subsets of objects which each satisfy the unimodality criterion within
each subset. The number of possible solutions across multiple solution subsets
is larger than $n!$, which underscores the need to find new algorithms and
heuristics to assist in the deterministic frequency seriation problem.
