A CAT algorithm for the exhaustive generation of ice piles

Abstract

We present a CAT (constant amortized time) algorithm for generating those partitions of n that are in the ice pile model (n), a generalization of the sand pile model (n). More precisely, for any fixed integer k, we show that the negative lexicographic ordering naturally identifies a tree structure on the lattice (n): this lets us design an algorithm which generates all the ice piles of (n) in amortized time O(1) and in space O( ).