A simple permutoassociahedron
Abstract
In the early 1990s, a family of combinatorial CW-complexes named permutoassociahedra was introduced by Kapranov, and it was realised by Reiner and Ziegler as a family of convex polytopes. The polytopes in this family are “hybrids” of permutohedra and associahedra. Since permutohedra and associahedra are simple, it is natural to search for a family of simple permutoassociahedra, which is still adequate for a topological proof of Mac Lane’s coherence. This paper presents such a family.
Keywords:
Associativity / Commutativity / Coherence / Simple polytopes / Geometric realisationSource:
Discrete Mathematics, 2019, 342, 12Publisher:
- Elsevier B.V.
Funding / projects:
- Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems (RS-174020)
- 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-44006)
- Representations of logical structures and formal languages and their application in computing (RS-174026)
Institution/Community
Arhitektonski fakultetTY - JOUR AU - Baralić, Djordje AU - Ivanović, Jelena AU - Petrić, Zoran PY - 2019 UR - https://raf.arh.bg.ac.rs/handle/123456789/1161 AB - In the early 1990s, a family of combinatorial CW-complexes named permutoassociahedra was introduced by Kapranov, and it was realised by Reiner and Ziegler as a family of convex polytopes. The polytopes in this family are “hybrids” of permutohedra and associahedra. Since permutohedra and associahedra are simple, it is natural to search for a family of simple permutoassociahedra, which is still adequate for a topological proof of Mac Lane’s coherence. This paper presents such a family. PB - Elsevier B.V. T2 - Discrete Mathematics T1 - A simple permutoassociahedron VL - 342 IS - 12 DO - 10.1016/j.disc.2019.07.007 ER -
@article{ author = "Baralić, Djordje and Ivanović, Jelena and Petrić, Zoran", year = "2019", abstract = "In the early 1990s, a family of combinatorial CW-complexes named permutoassociahedra was introduced by Kapranov, and it was realised by Reiner and Ziegler as a family of convex polytopes. The polytopes in this family are “hybrids” of permutohedra and associahedra. Since permutohedra and associahedra are simple, it is natural to search for a family of simple permutoassociahedra, which is still adequate for a topological proof of Mac Lane’s coherence. This paper presents such a family.", publisher = "Elsevier B.V.", journal = "Discrete Mathematics", title = "A simple permutoassociahedron", volume = "342", number = "12", doi = "10.1016/j.disc.2019.07.007" }
Baralić, D., Ivanović, J.,& Petrić, Z.. (2019). A simple permutoassociahedron. in Discrete Mathematics Elsevier B.V.., 342(12). https://doi.org/10.1016/j.disc.2019.07.007
Baralić D, Ivanović J, Petrić Z. A simple permutoassociahedron. in Discrete Mathematics. 2019;342(12). doi:10.1016/j.disc.2019.07.007 .
Baralić, Djordje, Ivanović, Jelena, Petrić, Zoran, "A simple permutoassociahedron" in Discrete Mathematics, 342, no. 12 (2019), https://doi.org/10.1016/j.disc.2019.07.007 . .