Gray codes for column-convex polyominoes and a new class of distributive lattices

Abstract

We introduce the problem of polyomino Gray codes, which is the listing of all members of certain classes of polyominoes such 4 that successive polyominoes differ by some well-defined closeness condition (e.g., the movement of one cell). We discuss various 5 closeness conditions and provide several Gray codes for the class of column-convex polyominoes with a fixed number of cells 6 in each column. For one of our closeness conditions, a natural new class of distributive lattice arises: the partial order is defined 7 on the set of m-tuples [S 1 ] × [S 2 ] × • • • × [S m ], where each S i > 1 and [S i ] = {0, 1,. .. , S i − 1}, and the cover relations are 8