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Reisdorf, Stephen R.Cellohedra
Master of Science, University of Akron, 2012, Mathematics
The associahedron has been generalized to a great variety of combinatorial structures. In each example the convex polytope is found whose face poset is the same as a certain poset structure on the combinatorial structures. Here we find polytopes whose face poset models the containment order of certain order ideals of the face poset of a cell complex. This is progress in a program which asks which posets in general have their ideals modeled by convex polytopes.

Committee:

Stefan Forcey, Dr. (Advisor); James P. Cossey, Dr. (Committee Member); Jeffrey Riedl, Dr. (Committee Member)

Subjects:

Mathematics

Keywords:

associahedra; associahedron; graph associahedra; graph associahedron; pseudograph associahedron; cell complex; geometric combinatorics; polytope; polytopes

Berry, Lisa TredwayPainted Trees and Pterahedra
Master of Science, University of Akron, 2013, 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.

Committee:

Stefan Forcey, Dr. (Advisor); W. Stuart Clary, Dr. (Committee Member); Hung Nguyen, Dr. (Committee Member)

Subjects:

Mathematics

Keywords:

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