The number of rhombus tilings of a "punctured" hexagon and the minor summation formula

Details The number of rhombus tilings of a "punctured" hexagon and the minor summation formula The number of rhombus tilings of a "punctured" hexagon and the minor summation formula

1997-11-26

arxiv.org/abs/math/9712203v1

Adv. Appl. Math. 21 1998, 381-404

Mathematics

Combinatorics

21 pages, AmS-TeX, uses TeXDraw

Scientific paper

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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