A method for the enumeration of various classes of column-convex polygons
Discrete Mathematics
Object grammars and bijections
Theoretical Computer Science
Enumeration of L-convex polyominoes by rows and columns
Theoretical Computer Science
Combinatorial aspects of L-convex polyominoes
European Journal of Combinatorics
| Hi-index | 5.23 |
In this paper, we consider the class of 4-stack polyominoes, i.e. polyominoes which can be decomposed into a central rectangle supporting four stack polyominoes, one on each side of the rectangle. This class of objects-recently introduced by Marc Noy-extends the class of centered convex polyominoes, and is included into the class of Z-convex polyominoes. Using an inclusion/exclusion approach, we obtain the enumeration of 4-stack polyominoes according to the number of rows and columns. Moreover, we solve some problems posed by Marc Noy, proving that the generating function of 4-stack polyominoes according to the semi-perimeter is algebraic, and that their asymptotic behavior is n4^n, which is immediately smaller than the asymptotic behavior of Z-convex polyominoes, which is n4^n. As a corollary of our result, we find the generating function of bi-centered polyominoes, i.e. convex polyominoes which are both horizontally and vertically centered.