Geodesic
A generalized Vandermonde determinant
Journal of Algebraic Combinatorics, Tome 1 (1992) no. 2, pp. 105-109.

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Summary: We prove two determinantal identities that generalize the Vandermondedeterminant identity $det( x _{ i} ^{ j} ) _{ i, j = 0, \frac{1}{4} , m}$ = Õ $_{0 \leqslant i j \leqslant m} ( x _{ j} - x _{ i} ) \det $(x_i^j )_i,j = 0, $\ldots ,m$ = prodlimits_$0 \leqslant $i j $\leqslant m$ (x_j - x_i ) . In the first of our identities the set ${0, \dots , m}$ indexing the rows and columns of thedeterminant is replaced by an arbitrary finite order ideal in the set ofsequences of nonnegative integers which are 0 except for a finite numberof components. In the second the index set is replaced by an arbitraryfinite order ideal in the set of all partitions.
Keywords: Vandermonde, determinant, partition, ideal 
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     title = {A generalized {Vandermonde} determinant},
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Buck, Marshall W.; Coley, Raymond A.; Robbins, David P. A generalized Vandermonde determinant. Journal of Algebraic Combinatorics, Tome 1 (1992) no. 2, pp. 105-109. http://geodesic.mathdoc.fr/item/JAC_1992__1_2_a5/