THE NUMBER OF RHOMBUS TILINGS OF A PUNCTURED HEXAGON AND THE MINOR SUMMATION FORMULA

We compute the number of all rhombus tilings of a hexagon with sides a , b + 1, c, a + 1, b, c + 1, of which the central triangle it; removed , provided a, b, c have the same parity. The result is B([a/2],[b/2], [c/2])B([(a + 1)/2],[b/2], [c/2])B([a/2], [(b + 1)/2], [c/2])B([a/2], [b/2],[(c + 1)/2]), where B(alpha, beta, gamma) is the number of plane partitions inside the alpha x beta x gamma box. The I,roof uses nonin tersecting lattice paths and a new identity for Schur functions, which is proved by means of the minor summation formula of Ishikawa and Wak ayama. [Proc. Japan Acad. Ser. A 71 (1995), 54-57]. A symmetric genera lization of this identity is stated as a conjecture. (C) 1998 Academic Press.