While the map from partitions to their Young diagrams is injective, this is not the case from the map from skew shapes to skew diagrams; therefore the shape of a skew diagram cannot always be determined from the set of filled squares only.
While the map from partitions to their Young diagrams is injective, this is not the case from the map from skew shapes to skew diagrams; therefore the shape of a skew diagram cannot always be determined from the set of filled squares only.