Ribbon Tile Invariants from Signed Area

Cristopher Moore and Igor Pak

To appear in J. Combin. Theory Ser. A

Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were first introduced in [Pak], where a full basis of invariants of ribbon tiles was conjectured. Here we present a complete proof of the conjecture, which works by associating ribbon tiles with a certain polygon in the complex plane, and deriving invariants from the signed area of this polygon.

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Cris Moore <moore@santafe.edu>