Cilanne Boulet

Learn More
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)
  • 1