Geometrical Realisations of the Simple Permutoassociahedron by Minkowski Sums

Applicable Analysis and Discrete Mathematics

article

Jelena Ivanović¹ 

[1] University of Belgrade, Faculty of Architecture Bulevar Kralja Aleksandra 73/II 11000 Belgrade

关键词: Minkowski sum;    geometrical realisation;    coherence;    simple polytopes;   

DOI  :  10.2298/AADM190414011I

学科分类：社会科学、人文和艺术（综合）

来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering

【 摘 要 】

This paper introduces a family of n-polytopes, P An,c which is a geometrical realisation of simple permutoassociahedra. It has significant importanceserving as a topological proof of Mac Lane’s coherence. Polytopes in thisfamily are defined as Minkowski sums of certain polytopes such that everysummand produces exactly one truncation of the permutohedron, i.e. yieldsto the appropriate facet of the resulting sum. Additionally, it leads to thecorrelation between Minkowski sums and truncations, which gives a generalprocedure for similar geometrical realisation of a wider class of polytopes.

【 授权许可】

Unknown