Rooks on Ferrers Boards and Matrix Integrals
نویسنده
چکیده
Let C(n; N) = R H N tr Z 2n (dZ) denote a matrix integral by a U(N)-invariant gaussian measure on the space H N of hermitian N N matrices. The integral is known to be always a positive integer. We derive a simple combinatorial interpretation of this integral in terms of rook conngurations on Ferrers boards. The formula C(n; N) = (2n ? 1)!! n X k=0 N k + 1 n k 2 k found by J. Harer and D. Zagier follows from our interpretation immediately.
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