Polyominoes with nearly convex columns: An undirected model

Abstract

Column-convex polyominoes were introduced in 1950's by Temperley, a mathematical physicist working on "lattice gases" By now, column-convex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes. However, the enumeration by area has been done for only one of the said generalizations, namely for multi-directed animals. In this paper, we introduce a new sequence of supersets of column-convex polyominoes. Our model (we call it level m column-subconvex polyominoes) is defined in a simple way: every column has at most two connected components and, if there are two connected components, the gap between them consists of at most m cells...