7,375 research outputs found
Gorenstein simplices and the associated finite abelian groups
It is known that a lattice simplex of dimension corresponds a finite
abelian subgroup of . Conversely, given a finite
abelian subgroup of such that the sum of all
entries of each element is an integer, we can obtain a lattice simplex of
dimension . In this paper, we discuss a characterization of Gorenstein
simplices in terms of the associated finite abelian groups. In particular, we
present complete characterizations of Gorenstein simplices whose normalized
volume equals and , where and are prime numbers with . Moreover, we compute the volume of the dual simplices of Gorenstein
simplices.Comment: 18 pages, to appear in European Journal of Combinatoric
Cayley sums and Minkowski sums of -convex-normal lattice polytopes
In this paper, we discuss the integer decomposition property for Cayley sums
and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley
sums have the integer decomposition property in terms of Minkowski sums.
Moreover, by using this characterization, we consider when Cayley sums and
Minkowski sums of -convex-normal lattice polytopes have the integer
decomposition property. Finally, we also discuss the level property for
Minkowski sums and Cayley sums.Comment: 10 page
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