Let x = {x1, . . . , xr}, y = {y1, . . . , yn}, z = {z1, . . . , zn} be three sets of indeterminates. We give the value of the determinant ∣ ∣ ∣ ∣ ∣ ∏ x∈x (xy − z) ∣ ∣ ∣ ∣ ∣ y∈y,z∈z when specializing y and z to the set of roots of yn − 1 and zn − ξn respectively. In the case where r = 2 and x = {1, 1} the determinant ∣ ∣(y− z) ∣ ∣ y∈y,z∈z factorizes into the determinant of the Cauchy matrix [(y...
