2012
DOI: 10.1088/1751-8113/45/31/315201
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Powers of the Vandermonde determinant, Schur functions and recursive formulas

Abstract: Since every even power of the Vandermonde determinant is a symmetric polynomial, we want to understand its decomposition in terms of the basis of Schur functions. We investigate several combinatorial properties of the coefficients in the decomposition. In particular, we give recursive formulas for the coefficient of the Schur function s µ in the decomposition of an even power of the Vandermonde determinant in n + 1 variables in terms of the coefficient of the Schur function s λ in the decomposition of the same… Show more

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Cited by 4 publications
(2 citation statements)
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“…Moreover, N 2 = 5, N 4 = 4, N 6 = 4, N 8 = 3. For more on (higher) powers of the Vandermonde, see, e.g., [ScThWy94,Ba11].…”
Section: Now Notice Thatmentioning
confidence: 99%
“…Moreover, N 2 = 5, N 4 = 4, N 6 = 4, N 8 = 3. For more on (higher) powers of the Vandermonde, see, e.g., [ScThWy94,Ba11].…”
Section: Now Notice Thatmentioning
confidence: 99%
“…Explicit algorithmic methods for expressing even powers of the Vandermonde determinant as combinations of Schur functions, and Laughlin wave functions as combinations of Slater functions, are discussed in [5], [61]. By analogy with the expression i (z i − z) p for a vortex of vorticity p centered at z, the Vandermonde determinant V (z 1 , .…”
Section: Laughlin-type Wave Functionsmentioning
confidence: 99%