The involution principle and h-positive symmetric functions
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/8225 |
| _version_ | 1826202718550622208 |
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| author | Joseph, Benjamin S., 1976- |
| author2 | Richard P. Stanley. |
| author_facet | Richard P. Stanley. Joseph, Benjamin S., 1976- |
| author_sort | Joseph, Benjamin S., 1976- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. |
| first_indexed | 2024-09-23T12:15:51Z |
| format | Thesis |
| id | mit-1721.1/8225 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T12:15:51Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/82252019-04-12T09:16:06Z The involution principle and h-positive symmetric functions Joseph, Benjamin S., 1976- 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, 2001. Includes bibliographical references (p. 65). The criterion of h-positivity corresponds to the criterion that a polynomial representation of the general linear group of V is a sum of tensor products of symmetric powers of V. Expanding the iterated exponential function as a power series yields coefficients whose positivity implies the h-positivity of the characteristic of the symmetric group character whose value on the permutation w is the number of labeled forests with c(w) vertices, where c(w) is the number of cycles of w. Another example of an h-positive symmetric function is the characteristic of the top homology of the even-ranked subposet of the partition lattice. In this case, the positive coefficients of the characteristic refine the tangent number E₂nâ₁ into sums of powers of two. by Benjamin S. Joseph. Ph.D. 2005-08-23T18:26:17Z 2005-08-23T18:26:17Z 2001 2001 Thesis http://hdl.handle.net/1721.1/8225 50147615 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 65 p. 3844151 bytes 3843908 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Joseph, Benjamin S., 1976- The involution principle and h-positive symmetric functions |
| title | The involution principle and h-positive symmetric functions |
| title_full | The involution principle and h-positive symmetric functions |
| title_fullStr | The involution principle and h-positive symmetric functions |
| title_full_unstemmed | The involution principle and h-positive symmetric functions |
| title_short | The involution principle and h-positive symmetric functions |
| title_sort | involution principle and h positive symmetric functions |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/8225 |
| work_keys_str_mv | AT josephbenjamins1976 theinvolutionprincipleandhpositivesymmetricfunctions AT josephbenjamins1976 involutionprincipleandhpositivesymmetricfunctions |