We present a complete classification of SL(n) contravariant, C(Rⁿ\)-valued valuations on polytopes, without any additional assumptions.It extends the previous results of the second author [Int. Math. Res. Not. 2020] which have a good connection with the Lₚ and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of SL(n) contravariant symmetric-tensor-valued valuations on polytopes.
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Tang et al. (2024) studied this question.
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