On Translating One Polyomino To Tile the Plane.
Permutations defining convex permutominoes.
Polyiamonds and polyhexes with minimum site-perimeter and achievement games.
Proof trees for weak achievement games.
Shape tiling.
Snaky is a 41-dimensional winner.
Succession rules and deco polyominoes
Succession rules and Deco polyominoes
In this paper, we examine the class of "deco" polyominoes and the succession rule describing their construction. These polyominoes are enumerated according to their directed height by factorial numbers. By changing some aspects of the "factorial" rule, we obtain some succession rules that describe various "deco" polyomino subclasses. By enumerating the subclasses according to their height and width, we find the following well-known numbers: Stirling numbers of the first and second kind,...
The code problem for directed figures
We consider directed figures defined as labelled polyominoes with designated start and end points, with two types of catenation operations. We are especially interested in codicity verification for sets of figures, and we show that depending on the catenation type the question whether a given set of directed figures is a code is decidable or not. In the former case we give a constructive proof which leads to a straightforward algorithm.
The code problem for directed figures
We consider directed figures defined as labelled polyominoes with designated start and end points, with two types of catenation operations. We are especially interested in codicity verification for sets of figures, and we show that depending on the catenation type the question whether a given set of directed figures is a code is decidable or not. In the former case we give a constructive proof which leads to a straightforward algorithm.
The dimer problem for narrow rectangular arrays: A unified method of solution, and some extensions.
The height of directed column-convex polyominoes. (La hauteur des polyominos dirigés verticalement convexe.)
The three dimensional polyominoes of minimal area.
The umbral transfer-matrix method. III: Counting animals.
The umbral transfer-matrix method. IV: Counting self-avoiding polygons and walks.
Three classes of diameter edge-invariant graphs
Tilings and isoperimetrical shapes I: Square lattice
Tilings by translation: enumeration by a rational language approach.
Une bijection entre les polyominos convexes dirigés et les mots de Dyck bilatères