Existence of regular unimodular triangulations of dilated empty simplices

摘要

Given integers k and m with k = 2 and m = 2, let P be an empty simplex of dimension (2k - 1) whose delta-polynomial is of the form 1 + (m - 1)t(k). In the present paper, the necessary and sufficient condition for the kth dilation kP of P to have a regular unimodular triangulation will be presented. (C) 2018 Elsevier Ltd. All rights reserved.