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The Relationship between the Stasheff Polytope and Painted Trees Using Tubings | ||
| Engineering and Technology Journal | ||
| Article 1, Volume 34, 1B, 2016, Pages 46-58 PDF (1023.84 K) | ||
| DOI: 10.30684/etj.34.1B.5 | ||
| Authors | ||
| Shatha Asaad Salman; Anwar Khaleel Faraj; Alaa Sabeeh Dawood | ||
| Abstract | ||
| A polytope plays a central role in different areas of mathematics. It is used quite heavily in applied fields of mathematics, such as medical imaging and robotics, geometric modeling. A polytope has many users in modern science such as computer graphics, optimization, and search engine. It is intended for a broad audience of mathematically inclined. Therefore in this paper, we shall take a polytope with one kind of application, which is known as a Stasheff polytope. it has been applied in: moduli spaces, Erhart polynomial, physics- chemistry, and Hopf algebras. In this paper,a finite graph G with tubingis taken, the nodes of the graph are reducetopoints in R^n and the convex hull for them are simplex, permutahedron and associahedron (Stasheff polytope ) are studied. Also, a fan graph to the painted tree is also taken and reduces its nodes to points inR^n. The converse of this result is also given with different examples to consult our results. | ||
| Keywords | ||
| Stasheff Polytope; Permutohedron; Tube; Tubing; Painted tree; fan graph | ||
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