2026-09-19T04:48:21Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/311622022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Richard P. Stanley.
Boulet, Cilanne Emily
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-02-02T18:54:15Z
2006-02-02T18:54:15Z
2005
2005
http://hdl.handle.net/1721.1/31162
61212230
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (p. 81-83).
In this thesis, we present bijections proving partitions identities. In the first part, we generalize Dyson's definition of rank to partitions with successive Durfee squares. We then present two symmetries for this new rank which we prove using bijections generalizing conjugation and Dyson's map. Using these two symmetries we derive a version of Schur's identity for partitions with successive Durfee squares and Andrews' generalization of the Rogers-Ramanujan identities. This gives a new combinatorial proof of the first Rogers-Ramanujan identity. We also relate this work to Garvan's generalization of rank. In the second part, we prove a family of four-parameter partition identities which generalize Andrews' product formula for the generating function for partitions with respect number of odd parts and number of odd parts of the conjugate. The parameters which we use are related to Stanley's work on the sign-balance of a partition.
by Cilanne Emily Boulet.
Ph.D.
83 p.
3562507 bytes
3571381 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Partition identity bijections related to sign-balance and rank
Thesis
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