6 JOSEPH ZAKS
Therefore
(5) a =
XQJ.
Theorem 9 of [2, p. 186] implies
(6) 0 x
0 1
2.
By counting the total number of the nonzero terms of B(F), in two ways (rows and
columns), we easily get (see [17]) the following.
(7) X (i+j)xy = 36 .
ij
Property (2) of B(F) implies that every two rows contributes exactly one minor of the form
(X?)-
thus there are 36 (= 9-8/2) such minors. On the other hand, each column counted by xy
contributes i-j such minors, hence we have
(8) X ijxij = 36 .
ijl
It is worth mentioning, as we already did in [17], that the system of equations (7) and (8)
is equivalent to the relations obtained by Baston [2] in connection with his notion of "surplus".
Let us define a (possibly multi-) graph G, having the nine vertices {1, 2,..., 9}. A vertex i
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