Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5777337 | European Journal of Combinatorics | 2018 | 13 Pages |
Abstract
It is known that a lattice simplex of dimension d corresponds a finite abelian subgroup of (RâZ)d+1. Conversely, given a finite abelian subgroup of (RâZ)d+1 such that the sum of all entries of each element is an integer, we can obtain a lattice simplex of dimension d. 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 p,p2 and pq, where p and q are prime numbers with pâ q. Moreover, we compute the volume of the associated dual reflexive simplices of the Gorenstein simplices.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Akiyoshi Tsuchiya,