A combinatorial method for the enumeration of column-convex polyominoes
نویسندگان
چکیده
منابع مشابه
Enumeration of convex polyominoes using the ECO method
ECO is a method for the enumeration of classes of combinatorial objects based on recursive constructions of such classes. In the first part of this paper we present a construction for the class of convex polyominoes based on the ECO method. Then we translate this construction into a succession rule. The final goal of the paper is to determine the generating function of convex polyominoes accord...
متن کاملCombinatorial aspects of L-convex polyominoes
We consider the class of L-convex polyominoes, i.e. those polyominoes in which any two cells can be connected with an “L” shaped path in one of its four cyclic orientations. The paper proves bijectively that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the linear recurrence relation fn+2 = 4 fn+1 − 2 fn , by first establishing a recurrence of the same form for the car...
متن کاملOn the enumeration of column-convex permutominoes
We study the enumeration of column-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations. We provide a direct recursive construction for the column-convex permutominoes of a given size, based on the application of the ECO method and generating trees, which leads to a functional equation. Then we obtain some upper and lower bounds for the number of column-convex ...
متن کاملA method for the enumeration of various classes of column-convex polygons
2 Abstract. We present a new method that allows to enumerate various classes of column-convex polygons, according to their perimeter and their area. The rst step of this method leads to a functional equation which deenes implicitly the generating function of the class under consideration. The second step consists in solving this equation. We apply systematically our method to all the usual clas...
متن کاملEnumeration of generalized polyominoes
As a generalization of polyominoes we consider edge-to-edge connected nonoverlapping unions of regular k-gons. For n ≤ 4 we determine formulas for the number ak(n) of generalized polyominoes consisting of n regular k-gons. Additionally we give a table of the numbers ak(n) for small k and n obtained by computer enumeration. We finish with some open problems for k-polyominoes.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1996
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)00310-f