  Many information sources are not just sequences of distinguishable symbols
but rather have invariances governed by alternative counting paradigms such as
permutations, combinations, and partitions. We consider an entire
classification of these invariances called the twelvefold way in enumerative
combinatorics and develop a method to characterize lossless compression limits.
Explicit computations for all twelve settings are carried out for i.i.d.
uniform and Bernoulli distributions. Comparisons among settings provide
quantitative insight.
