Root polytopes, triangulations, and subdivision algebras
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/60199 |
| _version_ | 1826210647211245568 |
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| author | Mészáros, Karola |
| author2 | Richard P. Stanley. |
| author_facet | Richard P. Stanley. Mészáros, Karola |
| author_sort | Mészáros, Karola |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. |
| first_indexed | 2024-09-23T14:52:56Z |
| format | Thesis |
| id | mit-1721.1/60199 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:52:56Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/601992019-04-10T12:57:55Z Root polytopes, triangulations, and subdivision algebras Mészáros, Karola Richard P. Stanley. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 99-100). In this thesis a geometric way to understand the relations of certain noncommutative quadratic algebras defined by Anatol N. Kirillov is developed. These algebras are closely related to the Fomin-Kirillov algebra, which was introduced in the hopes of unraveling the main outstanding problem of modern Schubert calculus, that of finding a combinatorial interpretation for the structure constants of Schubert polynomials. Using a geometric understanding of the relations of Kirillov's algebras in terms of subdivisions of root polytopes, several conjectures of Kirillov about the reduced forms of monomials in the algebras are proved and generalized. Other than a way of understanding Kirillov's algebras, this polytope approach also yields new results about root polytopes, such as explicit triangulations and formulas for their volumes and Ehrhart polynomials. Using the polytope technique an explicit combinatorial description of the reduced forms of monomials is also given. Inspired by Kirillov's algebras, the relations of which can be interpreted as subdivisions of root polytopes, commutative subdivision algebras are defined, whose relations encode a variety of possible subdivisions, and which provide a systematic way of obtaining subdivisions and triangulations. by Karola Mészáros. Ph.D. 2010-12-06T17:37:01Z 2010-12-06T17:37:01Z 2010 2010 Thesis http://hdl.handle.net/1721.1/60199 681960519 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 100 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Mészáros, Karola Root polytopes, triangulations, and subdivision algebras |
| title | Root polytopes, triangulations, and subdivision algebras |
| title_full | Root polytopes, triangulations, and subdivision algebras |
| title_fullStr | Root polytopes, triangulations, and subdivision algebras |
| title_full_unstemmed | Root polytopes, triangulations, and subdivision algebras |
| title_short | Root polytopes, triangulations, and subdivision algebras |
| title_sort | root polytopes triangulations and subdivision algebras |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/60199 |
| work_keys_str_mv | AT meszaroskarola rootpolytopestriangulationsandsubdivisionalgebras |