Efficient generation of combinatorial objects is a well-researched
area. Among them many literature devoted on the combinatorial Gray
code approach where the goal is to find a Hamiltonian path or cycle
in a representative graph of the corresponding combinatorial class.
Another approach namely genealogical tree approach has been
recently introduced where the goal is to find a rooted spanning
tree in the representative graph. Researchers have also focused on
finding general patterns in the generation techniques of
combinatorial classes so that common approaches can be applied to a
large number of related problems. Here, we propose a unifying
framework for combinatorial generation by giving recursive
definition of an abstract combinatorial class. The definition can
be instantiated to an array of specific combinatorial classes
namely n-tuple, combination, integer partition, set partition and
binary trees by specifying the framework parameters appropriately.
As an illustration, we show the instantiation of the combinatorial
class of n-tuples, combinations and balanced parenthesis strings
and also give novel constant-time generation algorithm for each of
them.
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