Geodesic
Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 1022-1035

Voir la notice de l'article provenant de la source Cambridge University Press

A lattice polytope is a polytope in whose vertices are all in . The volume of a lattice polytope P containing exactly k ≥ 1 points in d in its interior is bounded above by . Any lattice polytope in of volume V can after an integral unimodular transformation be contained in a lattice cube having side length at most n ̇ n ! V. Thus the number of equivalence classes under integer unimodular transformations of lattice poly topes of bounded volume is finite. If S is any simplex of maximum volume inside a closed bounded convex body K in having nonempty interior, then K⊆ ( n + 2)S — (n+ l)s where mS denotes a nomothetic copy of S with scale factor m, and s is the centroid of S.
DOI : 10.4153/CJM-1991-058-4
Mots-clés : 52A43, 11H06, 11P21 
Lagarias, Jeffrey C.; Ziegler, Günter M. Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice. Canadian journal of mathematics, Tome 43 (1991) no. 5, pp. 1022-1035. doi: 10.4153/CJM-1991-058-4
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