Combinatorial aspects of polytope slices
Name
862976320-MIT.pdf
Description
Full printable version
Size
2.54 MB
Format
Adobe PDF
Checksum (MD5)
8b8a630552551b1cbf8b278fc2d76741
Author(s)
Li, Nan, Ph. D. Massachusetts Institute of Technology
Advisor(s)
Richard P. Stanley.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
Abstract
We studies two examples of polytope slices, hypersimplices as slices of hypercubes and edge polytopes. For hypersimplices, the main result is a proof of a conjecture by R. Stanley which gives an interpretation of the Ehrhart h*-vector in terms of descents and excedances. Our proof is geometric using a careful book-keeping of a shelling of a unimodular triangulation. We generalize this result to other closely related polytopes. We next study slices of edge polytopes. Let G be a finite connected simple graph with d vertices and let PG C Rd be the edge polytope of G. We call PG decomposable if PG decomposes into integral polytopes PG+ and PG- via a hyperplane, and we give an algorithm which determines the decomposability of an edge polytope. Based on a sequence of papers by Ohsugi and Hibi, we prove that when PG is decomposable, PG is normal if and only if both PG+ and PG- are normal. We also study toric ideals of PG, PG+ and PG-. This part is joint work with Hibi and Zhang.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 69-70).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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