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 IPM(k)(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 IPM(k)(n): this lets us design an algorithm which generates all the ice piles of IPM(k)(n) in amortized time O(1) and in space O(root n).