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发帖数: 5600 | 1 Let A = (q^n-1)(q^n -q^2 )...(q^n-q^(n-1))
B = q^{n(n-1)/2} (q-1)^n
Then # of max chains = A/B
Reason: A = # of vector ( e1, ..., en) which spans the whole
space
B = # of vectors in each equivalent class
( 2 such vectors in an equivalent class can be
obtained
from one to another by a linear
transformation, which
happens to be uniquely represented by a
nonsingular
lower triangular matrix).
Example, n=2, # = q+1.
-Z. |
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