Between graphical zonotope and graph-associahedron
Abstract
This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph and the last is the graph–associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to H–polytopes.
Keywords:
generalized permutohedron / quasisymmetric function / graph / decorated graph / combinatorial Hopf algebra / f−polynomialSource:
Turkish Journal of Mathematics, 2023Publisher:
- Turkish Journal of Mathematics
Funding / projects:
- Topology, geometry and global analysis on manifolds and discrete structures (RS-MESTD-Basic Research (BR or ON)-174034)
- GWORDS - Graphical Languages (RS-ScienceFundRS-Ideje-7749891)
Collections
Institution/Community
GraFarTY - JOUR AU - Pešović, Marko AU - Stojadinović, Tanja PY - 2023 UR - https://grafar.grf.bg.ac.rs/handle/123456789/3110 AB - This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph and the last is the graph–associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to H–polytopes. PB - Turkish Journal of Mathematics T2 - Turkish Journal of Mathematics T1 - Between graphical zonotope and graph-associahedron DO - mat-2304-5 ER -
@article{ author = "Pešović, Marko and Stojadinović, Tanja", year = "2023", abstract = "This manuscript introduces a finite collection of generalized permutohedra associated to a simple graph. The first polytope of this collection is the graphical zonotope of the graph and the last is the graph–associahedron associated to it. We describe the weighted integer points enumerators for polytopes in this collection as Hopf algebra morphisms of combinatorial Hopf algebras of decorated graphs. In the last section, we study some properties related to H–polytopes.", publisher = "Turkish Journal of Mathematics", journal = "Turkish Journal of Mathematics", title = "Between graphical zonotope and graph-associahedron", doi = "mat-2304-5" }
Pešović, M.,& Stojadinović, T.. (2023). Between graphical zonotope and graph-associahedron. in Turkish Journal of Mathematics Turkish Journal of Mathematics.. https://doi.org/mat-2304-5
Pešović M, Stojadinović T. Between graphical zonotope and graph-associahedron. in Turkish Journal of Mathematics. 2023;. doi:mat-2304-5 .
Pešović, Marko, Stojadinović, Tanja, "Between graphical zonotope and graph-associahedron" in Turkish Journal of Mathematics (2023), https://doi.org/mat-2304-5 . .