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arXiv · 2606.19986

Polynomial valuations on plane polygons

Askold Khovanskii·Valentina Kiritchenko·Vladlen Timorin
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Abstract

Scissors congruence problems involving translations have prompted the study of translation invariant simple valuations. We review this classical theory from a naive and consistent viewpoint: starting from a description of all simple valuations on polygons, we characterize the effect of translation invariance. A description of all polynomial simple valuations is obtained as a bi-product of the adopted approach and as a direct generalization of the translation invariant theory; it appears to be new.

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Askold Khovanskii, Valentina Kiritchenko, Vladlen Timorin. 2026-06-18. Polynomial valuations on plane polygons. https://arxiv.org/abs/2606.19986

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