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Painted Trees and Pterahedra
Berry, Lisa Tredway

2013, Master of Science, University of Akron, Mathematics.
Associahedra can be realized by taking the convex hull of coordinates derived from binary trees. Similarly, permutahedra can be found using leveled trees. In this paper we will introduce a new type of painted tree, (T ◦ Y)n where n is the number of interior nodes. We create these painted trees by composing binary trees on leveled trees. We define a coordinate system on these trees and take the convex hull of these points. We explore the resulting polytope and prove, using a bijection to tubings, that for n ≤ 4 the poset of the painted face trees with n+1 leaves is isomorphic to the face poset of an n-dimensional polytope, specifically KF1,n, the graph-associahedron for a fan graph, F1,n.
Stefan Forcey, Dr. (Advisor)
W. Stuart Clary, Dr. (Committee Member)
Hung Nguyen, Dr. (Committee Member)
111 p.

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Berry, L. (2013). Painted Trees and Pterahedra. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Berry, Lisa. "Painted Trees and Pterahedra." Electronic Thesis or Dissertation. University of Akron, 2013. OhioLINK Electronic Theses and Dissertations Center. 15 Dec 2017.

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Berry, Lisa "Painted Trees and Pterahedra." Electronic Thesis or Dissertation. University of Akron, 2013. https://etd.ohiolink.edu/

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