11 search results - page 2 / 3 » A Bijective Proof of Borchardt's Identity |
JCT
2006
13 years 4 months ago
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 direc...
JCT
2007
13 years 4 months ago
2007
In answer to a question of Andrews about finding combinatorial proofs of two identities in Ramanujan’s “lost” notebook, we obtain weighted forms of Euler’s theorem on part...
DAM
1998
13 years 4 months ago
1998
We give a simple and natural proof of (an extension of) the identity P(k, l, n) = P2(k − 1, l − 1, n − 1). The number P(k, l, n) counts noncrossing partitions of {1, 2, . . ...
JCT
2011
12 years 11 months ago
2011
We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k − 2 equals the number of overpartitions of n with non-overlined parts not con...
JCT
2007
13 years 4 months ago
2007
We define the notions of successive ranks and generalized Durfee squares for overpartitions. We show how these combinatorial statistics give extensions to overpartitions of combin...