A general exhaustive generation algorithm for Gray structures

A CAT algorithm for the exhaustive generation of ice piles

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model IPMk(n), a generalization of the sand pile model SPM(n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice IPMk(n): this lets us design an algorithm which generates all the ice piles ...

m-compositions and m-partitions: exhaustive generation and Gray code

In this paper we give an exhaustive generation algorithm for the class of m-compositions of integers with fixed m. Moreover we define a Gray code to list these combinatorial objects according to a particular order. Finally, we define m-partitions, which are an m-dimensional generalization of integer partitions, and an exhaustive generation algorithm for m-partitions, based on the same ideas use...

An exhaustive generation algorithm for Catalan objects and others

The paper presents a CAT generation algorithm for Dyck paths with fixed length n. It is the formalization of a method for the exhaustive generation of these paths which can be described by two equivalent strategies. The former uses a rooted tree, the latter lists the paths and provides a visit of the nodes of the tree, basing on three simple operations. These constructions are strictly connecte...

Exhaustive generation of gominoes

Isomorph-Free Exhaustive Generation

We describe a very general technique for generating families of combinatorial objects without isomorphs. It applies to almost any class of objects for which an inductive construction process exists. In one form of our technique, no explicit isomorphism testing is required. In the other form, isomorph testing is restricted to within small subsets of the entire set of objects. A variety of differ...