Ribbon Tile Invariants from Signed Area
نویسندگان
چکیده
Ribbon tiles are polyominoes consisting of n squares laid out in a path, each step of which goes north or east. Tile invariants were rst introduced in P1], 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 certain polygons in the complex plane, and deriving invariants from the signed area of these polygons.
منابع مشابه
Ribbon Tile Invariants
Let T be a finite set of tiles, and B a set of regions Γ tileable by T. We introduce a tile counting group G(T,B) as a group of all linear relations for the number of times each tile τ ∈ T can occur in a tiling of a region Γ ∈ B. We compute the tile counting group for a large set of ribbon tiles, also known as rim hooks, in a context of representation theory of the symmetric group. The tile cou...
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