Séminaire Lotharingien de Combinatoire, B61Ai (2010), 6 pp.

Alain Lascoux

Generalization of Scott's Permanent Identity

Abstract. Let x={x1,...,xr}, y={y1,...,yn}, z={z1,...,zn} be three sets of indeterminates. We give the value of the determinant

$\displaystyle \Bigg\vert \prod_{x\in \x} (xy-z)^{-1} \Bigg\vert _{y\in\y,
 z\in\z} $

when specializing y and z to the set of roots of yn-1 and zn-ξn, respectively.

Received: March 2, 2010. Accepted: April 13, 2010.

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