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SL(n) Contravariant Vector Valuations

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Abstract

All \(\mathrm{SL}(n)\) contravariant vector valuations on polytopes in \({\mathbb {R}}^n\) are completely classified without any additional assumptions. The facet vector is defined. It turns out to be the unique class of such valuations for \(n\ge 3\). In dimension two, the classification corresponds to the known case of \(SL (2)\) covariant valuations.

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Acknowledgements

The work of the first author was supported in part by the Austrian Science Fund (FWF M2642 and I3027) and by the National Natural Science Foundation of China (Project 11671249). The work of the second author was supported in part by the National Natural Science Foundation of China (Project 11701373) and by the Shanghai Sailing Program 17YF1413800. The second author is the corresponding author.

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Correspondence to Dan Ma.

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Li, J., Ma, D. & Wang, W. SL(n) Contravariant Vector Valuations. Discrete Comput Geom 67, 1211–1228 (2022). https://doi.org/10.1007/s00454-021-00335-y

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  • DOI: https://doi.org/10.1007/s00454-021-00335-y

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