According to this proposition we can easily translate the previous succession rule in the following system of functional equations for the generating functions of the classes A, B, C and D.
As before, let l([pi]) denote the number of initial double points, h([pi]) = k([pi]) + l([pi]), and m([pi]) be the number of non initial double points: we need to refine the parameter h of our first succession rule by distinguishing the contribution of double points in the active region.
This gives the following contribution to the succession rule, according to the refined multilabel (k, l, m, [alpha], [beta], [gamma], [delta]):
Reconsidering all the special cases leads to the following complete succession rule (in sequences of multilabels of the same shape, bold symbols are used to emphasize parameters that fluctuate):
Proposition 3 Any succession rule of type [(p, q, r, s).
Succession rules may, therefore, be situationally determined and include various types of internal and external successions.
If a designated heir is adequately prepared or if the horse race is far enough along to have produced a clear leader, then the board may be able to follow the normal succession rules and promote the candidate.
In our sample, the normal succession process that would be consistent with succession rules may not be applicable.
Under current succession rules
, only male offspring can ascend to the imperial throne, meaning that if the 37-year-old princess gives birth to a boy, he will be second in line to the imperial throne after his father, Crown Prince Naruhito, 41.