Abstract
Km+n(x1 , . . . , xm+n)Kl(xm+1 , . . . , xm+l)−Km+l(x1 , . . . , xm+l)Kn(xm+1 , . . . , xm+n) = (−1)Km−1(x1 , . . . , xm−1)Kn−l−1(xm+l+2 , . . . , xm+n), m ≥ 1, l ≥ 0, n ≥ l + 1. (1) It is usually verified by induction on two out of the three parameters l , m, n . The proof given in the present paper is based on the fact that the determinant of a skew-symmetric 4×4 matrix (just as of any matrix of even order) is the square of some polynomial (the Pfaffian of the matrix):
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