From Object grammars to ECO method

In this paper we make a comparison between two methods for the enumeration of combinatorial objects, namely the ECO method and object grammars, both based on a recursive description for the examined class of objects. In particular, we study the problem of passing from an object grammar to an "equivalent" ECO system. First, we solve this problem for any unidimensional, unambiguous, and complete object grammar, with any linear parameter. Then we treat the more complex cases of q-linear parameters, and of multidimensional object grammars, giving some explanatory examples. In particular, we determine a new ECO system for the class of directed convex polyominoes. © 2003 Elsevier B.V. All rights reserved.