A Partition Theory of Planar Animals
Kenneth W. Holladay · Studies in Applied Mathematics · 1980
A dissection of an animal is a partition of its cells into blocks that are themselves animals. Then‐rule allows only those dissections with the area of every block a multiple ofn. If an animal with area divisible bynhas no dissection allowed by then‐rule, then the animal is said to be ann‐irreducible. The partition meet of all allowed dissections of a given animal is called then‐dissection residue of that animal. This paper considers only planar animals. All 2‐irreducibles are found, and the problem of computing 2‐dissection residues is solved. Two theorems onn‐irreducibles are proved. One of them states that largen‐irreducibles always arise by adding cells to smallern‐irreducibles.