2026-09-19T04:56:11Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/478992022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Richard Stanley.
Qing, Yulan, S.M. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2009-10-01T16:00:57Z
2009-10-01T16:00:57Z
2008
2008
http://hdl.handle.net/1721.1/47899
436221569
Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.
Includes bibliographical references (leaf 53).
In this thesis I study r-differential posets and dual graded graphs. Differential posets are partially ordered sets whose elements form the basis of a vector space that satisfies DU-UD=rI, where U and D are certain order-raising and order-lowering operators. New results are presented related to the growth and classification of differential posets. In particular, we prove that the rank sequence of an r-differential poset is bounded above by the Fibonacci sequence and that there is a unique poset with such a maximum rank sequence. We also prove that a 1-differential lattice is either Young's lattice or the Fibonacci lattice. In the second part of the thesis, we present a series of new examples of dual graded graphs that are not isomorphic to the ones presented in Fomin's original paper.
by Yulan Qing.
S.M.
53 leaves
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Differential posets and dual graded graphs
Thesis
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