Applying this rule recursively will result in a tree of character value evaluations for smaller and smaller partitions. Each branch stops for one of two reasons: Either there are no border strips of the required length within the reduced shape, so the sum on the right is zero, or a border strip occupying the entire reduced shape is removed, leaving a Young diagram with no boxes. At this point we are evaluating χ ρ when both λ and ρ are the empty partition (), and the rule requires that this terminal case be defined as having character χ χ ( ) ( ) = 1 .