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 of IPMk(n) in amortized time O(1) and in space O( √ n). Mathematics Subject Classification. 05A17, 68R99.