Figure 10: Generic (2,3/2) de Bruijn diagram.
By the third stage the staircase is fully evident; each step contains k 1's, likewise there are k staircases:
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The minimal equation is readily determined to be 
,
and as before the Jordan normal form prevails.
There are two interesting factorizations, both of which are quite
general: 
according to
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and 
according to
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Several relationships among these matrices are evident; for example:
wherein I is the unit matrix. The factors satisfy several identities, of which the most useful are:
P and Q are noncommuting permutation matrices; nevertheless the noncommutative binomial theorem can still be used to evaluate powers of D. Whatever scheme is used, the essential observation is that powers of D exhibit broader steps and more numerous ladders until the matrix is solidly filled with 1's; from then on successive powers merely differ by the factor k.