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Polynomier og Young-diagrammer<br />
Et Young diagram µ giver anledning til et polynomium:<br />
p µ = det(x p j<br />
i<br />
y q j<br />
i<br />
) 1≤i,j≤n ,<br />
hvor (p j , q j ) 1≤j≤n<br />
betegner koordinaterne hørende til Young<br />
diagrammet.<br />
Eksempel : Polynomiet hørende til Young-diagrammet<br />
µ = (0,1)<br />
(0,0) (1,0)<br />
er<br />
⎛<br />
x1 0y 1 0 x1 1y 1 0 x1 0y 1 ⎞ ⎛ ⎞<br />
1 1 x 1 y 1<br />
p µ = det ⎝x2 0y 2 0 x2 1y 2 0 x2 0y 2<br />
1 ⎠ = det ⎝1 x 2 y 2<br />
⎠<br />
x3 0y 3 0 x3 1y 3 0 x3 0y 3<br />
1 1 x 3 y 3
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