The number of rhombus tilings of a "punctured" hexagon and the minor summation formula
Soichi Okada, Christian Krattenthaler
Abstract
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 is removed, provided a,b,c have the same parity. The result is a product of four numbers, each of which counts the number of plane partitions inside a given box. The proof uses nonintersecting lattice paths and a new identity for Schur functions, which is proved by means of the minor summation formula of Ishikawa and Wakayama. A symmetric generalization of this identity is stated as a conjecture.
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