2026-09-18T21:25:30Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/389572022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Richard Stanley.
Pylyavskyy, Pavlo
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2007-09-28T13:18:50Z
2007-09-28T13:18:50Z
2007
2007
http://hdl.handle.net/1721.1/38957
166325714
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 71-74).
In this thesis a conjecture of Okounkov, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity of certain differences of products of Schur functions are proved. In the first part of the work a combinatorial method is developed that allows to prove weaker versions of those conjectures. In the second part a recent result of Rhoades and Skandera is used to provide a proof of actual Schur positivity results. Several further generalizations are stated and proved. In particular, an intriguing log-concavity property of Schur functions is observed. In addition, a stronger conjecture is stated in language of alcoved polytops. A weaker version of this conjecture is proved using a characterization of Klyachko cone and the theory of Temperley-Lieb immanants.
by Pavlo Pylyavskyy.
Ph.D.
74 p.
eng
Massachusetts Institute of Technology
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
Mathematics.
Comparing products of Schur functions and quasisymmetric functions
Thesis
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