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Article overview
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Lattice simplices of maximal dimension with a given degree | Akihiro Higashitani
; | Date: |
1 May 2016 | Abstract: | It was proved by Nill that for any lattice simplex of dimension $d$ with
degree $k$ which is not a lattice pyramid, the inequality $d leq 4k-2$ holds.
In this paper, we give a complete characterization of lattice simplices
satisfying the equality, i.e., the lattice simplices of dimension $(4k-2)$ with
degree $k$ which are not lattice pyramids. Moreover, we show that such
simplices are counterexamples for the conjecture known as "Cayley conjecture",
which says that every lattice polytope of dimension $d$ with degree less than
$d/2$ can be decomposed into a Cayley polytope of at least $(d+1-2k)$ lattice
polytopes. | Source: | arXiv, 1605.0273 | Services: | Forum | Review | PDF | Favorites |
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