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08 February 2025
 
  » arxiv » 1605.0273

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Lattice simplices of maximal dimension with a given degree
Akihiro Higashitani ;
Date 1 May 2016
AbstractIt 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
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