Differential posets and dual graded graphs
Citable URI:
http://hdl.handle.net/1721.1/47899
| Title: | Differential posets and dual graded graphs |
| Author: | Qing, Yulan, S.M. Massachusetts Institute of Technology |
| Other Contributors: | Massachusetts Institute of Technology. Dept. of Mathematics. |
| Advisor: | Richard Stanley. |
| Department: | Massachusetts Institute of Technology. Dept. of Mathematics. |
| Publisher: | Massachusetts Institute of Technology |
| Issue Date: | 2008 |
| Abstract: | 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. |
| Description: |
Thesis (S. M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008. Includes bibliographical references (leaf 53). |
| URI: | http://hdl.handle.net/1721.1/47899 |
| Keywords: | Mathematics. |
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