Another presentation of the problem
Let 2 :IRK IR be a continuously differentiable, strictly increasing
function in each of its arguments.
Let Q :R R be a continuously differentiable and strictly increas-
Let W :IRK IR be defined by composition as follows: W (x) ==
Let Wk denote the partial derivative of W with respect to xk.
For each k = 1, K, and all x, xe RK, let Dk be an order with the
following property: X Dk x' - W, (x) (x).
Suppose we know 2, the orders Dk and that W is defined by composition
as explained above (to be sure, we do not know the derivatives Wk (x) or
Wk (x'), only the sign of Wk (x) - W, (x')).
The questioni is: do we nevertheless have enough information to uniquely
recover Q (up to positive affine transformations)?
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