Polytope volume by descent in the face lattice and applications in social choice
Polytope volume by descent in the face lattice and applications in social choice
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DOI：
10.1007/s12532-020-00198-z
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发表时间：
2020-11-18
影响因子：
6.3
通讯作者：
Ichim, Bogdan
中科院分区：
文献类型：
--
作者：
Bruns, Winfried;Ichim, Bogdan
我们描述了在面格中通过下降来计算多面体体积，它在normalize中的实现，以及与逆字典三角剖分的联系。通过若干不同特征的高维多面体验证了该算法的有效性。最后，我们给出了一个在投票理论中的应用，其中多面体表现为某些悖论的概率。
We describe the computation of polytope volumes by descent in the face lattice, its implementation in Normaliz, and the connection to reverse-lexicographic triangulations. The efficiency of the algorithm is demonstrated by several high dimensional polytopes of different characteristics. Finally, we present an application to voting theory where polytope volumes appear as probabilities of certain paradoxa.