Painted Trees and Pterahedra

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)_<i>n</i> where <i>n</i> 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 <i>n</i> ≤ 4 the poset of the painted face trees with <i>n</i>+1 leaves is isomorphic to the face poset of an <i>n</i>-dimensional polytope, specifically KF_1,<i>n</i>, the graph-associahedron for a fan graph, F_1,<i>n</i>.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

University of Akron

Year dc:date

2013

Author dc:creator

• Berry, Lisa Tredway

Contributors dc:contributor

• Forcey, Stefan

• Mathematics
• painted trees
• polytope
• pterahedra
• graph-associahedra
• tubings

Statement dc:rights

• unrestricted
• This thesis or dissertation is protected by copyright: all rights reserved. It may not be copied or redistributed beyond the terms of applicable copyright laws.

Language dc:language

English

Repository record dc:identifier

http://rave.ohiolink.edu/etdc/view?acc_num=akron1365772885

OAI identifier oai:identifier

oai:etd.ohiolink.edu:akron1365772885