Shape of Ferrers Graph

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Do the positions of the outer corners of a Ferrers Graph suffice to determine the partition uniquely? What about the inner corners?

Shape of Ferrers Graphs: the contour is a horizontal line on top, a vertical line on the left and a ragged rim from the southwest corner to the northeast corner.

There are two kinds of corners on the rim: outer corners and inner corners. The two endpoints of the rim are inner corners. The outer corners are squares that can be removed and it'll still be a Ferrers board. The inner corners are places where squares can be added and a new Ferrers board is formed.