3 papers
math.CO2006
Dyson's new symmetry and generalized Rogers-Ramanujan identities
Cilanne Boulet
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 ass…
math.CO2004
A combinatorial proof of the Rogers-Ramanujan and Schur identities
Cilanne Boulet, Igor Pak
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 bij…
math.CO2003
A Four-parameter Partition Identity
Cilanne E. Boulet
We present a new partition identity and give a combinatorial proof of our result. This generalizes a result of Andrew's in which he considers the generation function for partitions…