Combinatorial Exploration: An Algorithmic Framework for Enumeration
Submitted
Michael, Christian, Anders, Émile, Jay and Henning
A combinatorial class is often studied by finding a combinatorial specification
for it, which is a description of the class in terms of simpler classes, and
perhaps recursions to smaller instances of the original class.
In this paper we describe how to automate the discovery of combinatorial specifications
of combinatorial classes. This is achieved by first generating a universe of
interconnected combinatorial classes and then searching for a specification
inside this universe. The main application is in the area of permutation
patterns, but other domains such as, set partitions, strings, polyominoes and
lattice paths are discussed considered.