Differential posets and dual graded graphs
Author(s)Qing, Yulan, S.M. Massachusetts Institute of Technology
Massachusetts Institute of Technology. Dept. of Mathematics.
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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.
Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliographical references (leaf 53).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology