Papers › The cyclicity rank of empty lattice simplices
The cyclicity rank of empty lattice simplices
Lukas Abend, Matthias Schymura
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We are interested in algebraic properties of empty lattice simplices Δ, that is, d-dimensional lattice polytopes containing exactly d+1 points of the integer lattice ℤᵈ. The cyclicity rank of Δ is the minimal number of cyclic subgroups that the quotient group of Δ splits into. It is known that up to dimension d ≤4, every empty lattice d-simplex is cyclic, meaning that its cyclicity rank is at most 1. We determine the maximal possible cyclicity rank of an empty lattice d-simplex for dimensions d ≤8, and determine the asymptotics of this number up to a logarithmic term.
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