Search results for "ECO method"
showing 2 items of 2 documents
Enumeration of L-convex polyominoes by rows and columns
2005
In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.
ECO-generation for some restricted classes of compositions
2013
International audience; We study several restricted classes of compositions by giving one-to-one maps between them and different classes of restricted binary strings or pattern avoiding permutations. Inspired by the ECO method, new succession rules for these classes are presented. Finally, we obtain generating algorithms in Constant Amortized Time (CAT) for theses classes.