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A Partition Theory of Planar Animals

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A dissection of an animal is a partition of its cells into blocks that are themselves animals. The n‐rule allows only those dissections with the area of every block a multiple of n. If an animal with area divisible by n has no dissection allowed by the n‐rule, then the animal is said to be an n‐irreducible. The partition meet of all allowed dissections of a given animal is called the n‐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 on n‐irreducibles are proved. One of them states that large n‐irreducibles always arise by adding cells to smaller n‐irreducibles.
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Document Type: Research Article

Affiliations: University of Miami

Publication date: October 1, 1980

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