Co'(mA,) = (N'-N-k X Eq. 9.28
1M (1 M (M
\n L n2 k
GiiZ'K (, !A J + C[ki n2,rJ .
M M ]M M M
I I M M M
m^, mA ii n, L n j, n2,r "' nk, %
It is noted that Eq. 9.28 is only an example, not a definition. It must be adjusted based
upon r to reflect the number and location of the nonzero adjacent state contributions.
The values of the determinants PA' i' = Ip(mA)' - PT -1'I are given by
employing Eq. 9.28 in Eq. 9.26 (with r restricted as noted above). Further, the a -- 0+
limits of the -~ ii' -i' = IP(miA)' -I'I P.^' -I' are provided by using the a -> '0 lim-
its of the factors (2LP(i I n) 1) in Eq. 9.26. Those limits are provided by using either
Pi(i ] n) or P2'(i | n) depending upon whether the two or three-operator case is under
consideration.
It is instructive to apply these results to a simple example. The following para-
graphs do so for the one-bit problem with population size 2. These parameters
(L = 1, M = 2) imply that S = {0,1}, N = 2, S'= {(20),(11),(02)}, N' = 3,
SA' = {(20), (02)} and S' S' = {(11)}. Thus r is limited to
(00 o00 00' '00' 'oo'
re I 00, 10 01, 11 20, 02
00 00 00 00 00 0,
and the combinatorial determinant required for evaluation of the nonzero order
Co'(mA,r)'s for m, = (20) by Eq. 9.28 has the general form