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- Cilanne Emily Boulet, P. Stanley, +5 authors Kanchan Chandra
- 2005

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… (More)

where Par denotes the set of all partitions, |λ| denotes the size (sum of the parts) of λ, θ(λ) denotes the number of odd parts in the partition λ, and θ(λ) denotes the number of odd parts in the conjugate of λ. A combinatorial proof of Andrews’ result was found by Sills in [2]. In this paper, we generalize this result and provide a combinatorial proof of… (More)

- Cilanne Boulet, Igor Pak
- J. Comb. Theory, Ser. A
- 2006

We give a combinatorial proof of the first Rogers-Ramanujan identity by using two symmetries of a new generalization of Dyson’s rank. These symmetries are established by direct bijections.

- Kanchan Chandra, Cilanne Boulet, +6 authors Richard Stanley
- 2003

Comments Welcome 1 We are grateful to David Laitin, who collaborated with Kanchan Chandra on early versions of this chapter and has contributed to many of the insights here; to

We present a generalization, which we call (k, m)-rank, of Dyson’s notion of rank to integer partitions with k successive Durfee rectangles and give two combinatorial symmetries associated with this new definition. We prove these symmetries bijectively. Using the two symmetries we give a new combinatorial proof of generalized Roger-Ramanujan identities. We… (More)

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