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Painted Trees and Pterahedra

Berry, Lisa Tredway
http://rave.ohiolink.edu/etdc/view?acc_num=akron1365772885

Abstract Details

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.
Mathematics
painted trees; polytope; pterahedra; graph-associahedra; tubings

Recommended Citations

Citations

  • Berry, L. T. (2013). Painted Trees and Pterahedra [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1365772885

    APA Style (7th edition)

  • Berry, Lisa. Painted Trees and Pterahedra. 2013. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1365772885.

    MLA Style (8th edition)

  • Berry, Lisa. "Painted Trees and Pterahedra." Master's thesis, University of Akron, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1365772885

    Chicago Manual of Style (17th edition)

akron1365772885
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© 2013, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.