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