Enumeration of inscribed polyominos

Enumeration of minimal 3D polyominoes inscribed in a rectangular prism

We consider the family of 3D minimal polyominoes inscribed in a rectanglar prism. These objects are polyominos and so they are connected sets of unitary cubic cells inscribed in a given rectangular prism of size b×k×h and of minimal volume equal to b + k + h − 2. They extend the concept of minimal 2D polyominoes inscribed in a rectangle studied in a previous work. Using their geometric structur...

Counting Directed-convex Polyominoes According to Their Perimeter

An approach is presented for the enumeration of directed-convex polyominos that are not parallelogram polyominoes and we establish that there are ( 2n n−2 ) with a perimeter of 2n + 4. Finally using known results we prove that there are ( 2n n ) directed-convex polyominos with a perimeter of 2n + 4.

Enumeration of polyominoes inscribed in a rectangle

Polyominos and Perfect Graphs

Polyominos are useful for modelizing real-life problems. Many graphs can be associated with polyominos. Because some NP-problems become polynomial for the class of perfect graph, to know whether or not these graphs are perfect is important from an algorithmic point of view. In this paper we shall investigate the perfection of several of these graphs.

On 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 ...