Geodesic
Directed Graphs and the Jacobi-Trudi Identity
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1201-1210

Voir la notice de l'article provenant de la source Cambridge University Press

Let |aij |n×n denote the n × n determinant with (i, j)-entry aij , and hk = hk (x 1, ..., xn ) denote the kth-homogeneous symmetric function of x 1, ..., xn defined by where the summation is over all m 1, ..., mn ≧ 0 such that m 1 + ... + mn = k. We adopt the convention that hk = 0 for k < 0. For integers α 1 ≧ α 2 ... ≧ αn ≧ 0, the Jacobi-Trudi identity (see [6], [7]) states that In this paper we give a combinatorial proof of an equivalent identity, Theorem 1.1, obtained by moving the denominator on the RHS to the numerator on the LHS. 
Goulden, I. P. Directed Graphs and the Jacobi-Trudi Identity. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1201-1210. doi: 10.4153/CJM-1985-065-6
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