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This is only slightly more complicated: consider for example the term
,
Again, only those terms survive where
,...,
. We could have, e.g.,
and
in which case neither
nor
can't be among the
,...,
(this would yield zero overlap in
) and therefore
and
must be among
and
.
This means we get two possibilities for the permutation pairs
and
now: one with
and
, and the other with
and
. In the first case
,
,
,...,
which means the permutaton
is the same as
. In the second case,
is the same permutation as
apart from one additional swap of
and
: this means that
and therefore
The sum over all pairs
now again yields
Subsections
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Tobias Brandes
2005-04-26