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Abstract Polytopes from Nested Posets

Showers, Patrick J
http://rave.ohiolink.edu/etdc/view?acc_num=akron1386028871

Abstract Details

2013, Master of Science, University of Akron, Mathematics.
In this paper, we continue a study of polytopes built from nested objects as a generalization of graph associahedra. Here, we use special subsets of a given partially ordered set to construct the face lattice of an abstract polytope. By viewing the incidence structure of a graph as a partially ordered set, this approach yields, among other polytopes, all (pseudo)graph associahedra. We cover the prerequisite order theoretic notions and provide necessary information on abstract polytopes. This enables us to define and study the structure of poset associahedra, culminating in the fact that poset associahedra are abstract polytopes.
Stefan Forcey, Dr. (Advisor)
W. Stuart Clary, Dr. (Committee Member)
Jeffrey Riedl, Dr. (Committee Member)
52 p.
Mathematics
abstract polytopes, geometric combinatorics, associahedra

Recommended Citations

Citations

  • Showers, P. J. (2013). Abstract Polytopes from Nested Posets [Master's thesis, University of Akron]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=akron1386028871

    APA Style (7th edition)

  • Showers, Patrick. Abstract Polytopes from Nested Posets. 2013. University of Akron, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=akron1386028871.

    MLA Style (8th edition)

  • Showers, Patrick. "Abstract Polytopes from Nested Posets." Master's thesis, University of Akron, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=akron1386028871

    Chicago Manual of Style (17th edition)

akron1386028871
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© 2013, all rights reserved.
This open access ETD is published by University of Akron and OhioLINK.