Quantum jumps of normal polytopes. (English) Zbl 1351.52011
The authors introduce a partial order on the set of all normal polytopes in \(\mathbb R^d\) (by inclusion), denoted by NPol\((d)\). Further, they derive arithmetic bounds on arithmetic relations for it, called quantum jumps. Using the above methods the authors compute the first examples of maximal elements in NPol(4) and in NPol(5).
Reviewer: Oleg Karpenkov (Liverpool)
MSC:
| 52B20 | Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) |
| 11H06 | Lattices and convex bodies (number-theoretic aspects) |
| 52C07 | Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry) |
Software:
NormalizReferences:
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