Enumeration of 4-stack polyominoes

Enumeration 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.

Algebraic Languages and Polyominoes Enumeration

In this paper, the u.)e of algebraic ianguages theory in solving an open problem in combinatorics is shown. By constructing a bijection between convex polyominoes and words of an algebraic language, atjd bq solving the corresponding algebraic qstem, we proie that the number of convex polyominoes with perimeter 2n + 8 is (2n + I1 )4” -4(2n + 1 )t2,F).

Enumeration of Polyominoes for p4 Tiling

Polyominoes are the two dimensional shapes made by connecting n unit squares, joined along their edges. In this paper, we propose algorithms to enumerate polyominoes for p4 tiling, i.e., those covering the plane by only 90 degrees rotations around two rotation centers. The conventional methods are basically trial and error, i.e., they repeat generating polyominoes and checking whether the shape...

Enumeration of polyominoes inscribed in a rectangle

Generalized triangulations and diagonal-free subsets of stack polyominoes

For n 3, let n be the set of line segments between vertices in a convex n-gon. For j 1, a j-crossing is a set of j distinct and mutually intersecting line segments from n such that all 2j endpoints are distinct. For k 1, let n,k be the simplicial complex of subsets of n not containing any (k + 1)-crossing. For example, n,1 has one maximal set for each triangulation of the n-gon. Dress, Koolen, ...