Concatenation arguments and their applications to polyominoes and polycubes

Abstract

In this paper, we develop a method for setting lower and upper bounds on growth constants of polyominoes and polycubes whose enumerating sequences are so-called quasi sub- or super-multiplicative. The method is based on concatenation arguments, applied directly or recursively. Inter alia, we demonstrate the method on general polycubes, tree polyominoes and polycubes, and convex polyominoes.