Geometrical realisations of the simple permutoassociahedron by Minkowski sums
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This paper introduces a family of n-polytopes, P An,c which is a geometrical realisation of simple permutoassociahedra. It has significant importance
serving as a topological proof of Mac Lane’s coherence. Polytopes in this
family are defined as Minkowski sums of certain polytopes such that every
summand produces exactly one truncation of the permutohedron, i.e. yields
to the appropriate facet of the resulting sum. Additionally, it leads to the
correlation between Minkowski sums and truncations, which gives a general
procedure for similar geometrical realisation of a wider class of polytopes.
Keywords:
Coherence / Simple polytopes / Geometrical realisation / Minkowski sumSource:
Applicable Analysis and Discrete Mathematics, 2020, 14, 1, 55-93Publisher:
- Belgrade : University of Belgrade, Faculty of Electrical Engineering, Department of Applied Mathematics
Funding / projects:
- Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-44006)
Institution/Community
Arhitektonski fakultetTY - JOUR AU - Ivanović, Jelena PY - 2020 UR - https://raf.arh.bg.ac.rs/handle/123456789/1060 AB - This paper introduces a family of n-polytopes, P An,c which is a geometrical realisation of simple permutoassociahedra. It has significant importance serving as a topological proof of Mac Lane’s coherence. Polytopes in this family are defined as Minkowski sums of certain polytopes such that every summand produces exactly one truncation of the permutohedron, i.e. yields to the appropriate facet of the resulting sum. Additionally, it leads to the correlation between Minkowski sums and truncations, which gives a general procedure for similar geometrical realisation of a wider class of polytopes. PB - Belgrade : University of Belgrade, Faculty of Electrical Engineering, Department of Applied Mathematics T2 - Applicable Analysis and Discrete Mathematics T1 - Geometrical realisations of the simple permutoassociahedron by Minkowski sums VL - 14 IS - 1 SP - 55 EP - 93 DO - 10.2298/AADM190414011I ER -
@article{ author = "Ivanović, Jelena", year = "2020", abstract = "This paper introduces a family of n-polytopes, P An,c which is a geometrical realisation of simple permutoassociahedra. It has significant importance serving as a topological proof of Mac Lane’s coherence. Polytopes in this family are defined as Minkowski sums of certain polytopes such that every summand produces exactly one truncation of the permutohedron, i.e. yields to the appropriate facet of the resulting sum. Additionally, it leads to the correlation between Minkowski sums and truncations, which gives a general procedure for similar geometrical realisation of a wider class of polytopes.", publisher = "Belgrade : University of Belgrade, Faculty of Electrical Engineering, Department of Applied Mathematics", journal = "Applicable Analysis and Discrete Mathematics", title = "Geometrical realisations of the simple permutoassociahedron by Minkowski sums", volume = "14", number = "1", pages = "55-93", doi = "10.2298/AADM190414011I" }
Ivanović, J.. (2020). Geometrical realisations of the simple permutoassociahedron by Minkowski sums. in Applicable Analysis and Discrete Mathematics Belgrade : University of Belgrade, Faculty of Electrical Engineering, Department of Applied Mathematics., 14(1), 55-93. https://doi.org/10.2298/AADM190414011I
Ivanović J. Geometrical realisations of the simple permutoassociahedron by Minkowski sums. in Applicable Analysis and Discrete Mathematics. 2020;14(1):55-93. doi:10.2298/AADM190414011I .
Ivanović, Jelena, "Geometrical realisations of the simple permutoassociahedron by Minkowski sums" in Applicable Analysis and Discrete Mathematics, 14, no. 1 (2020):55-93, https://doi.org/10.2298/AADM190414011I . .