A Valuation-Theoretic Approach to Translative-Equidecomposability

2015/07/05 by Kusejko, Katharina, Parapatits, Lukas · 2 citations
#52B45 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1507.01227

Abstract

All simple translation-invariant valuations on polytopes are classified. As a direct consequence the well-known conditions for translative-equidecomposability are recovered. Furthermore, a simplified proof of the classification of continuous simple translation-invariant valuations is presented.

Cited by

• Non-continuous valuations on convex bodies and a new characterization of volume
• Invariants and equidecomposability in rings of polygons with sides of given directions

Related

• Minkowski Valuations and Generalized Valuations
• Convex valuations, from Whitney to Nash
• Translation invariant valuations on quasi-concave functions
• On the extendability by continuity of angular valuations on polytopes
• Combinatorial mixed valuations