On new results about partitions into parts congruent to ±1 (mod 5)

Abstract

Abstract. In this work we talk about some patterns on partitions considered by the 1 st Rogers-Ramanujan Identity. Looking for a new bijective proof for it, we have studied partitions into parts congruent to ±1 (mod 5) and have created a two-line matrix representation for them. By adding up their second line elements, we have obtained the number of parts of the related partitions. We classify the partitions according to the sum on the second row of the matrix associated to it and organize the data on a table, obtaining some partition identitities.

Partitions generated by Mock Theta Functions ρ(q), σ(q) and ν(q) and relations with partitions into distinct parts

“…By considering the First Roger-Ramanujan's Identity, for example, partitions into 2-distinct parts are also represented as two-line matrices in [6]. Concerning the other side of the identity, partitions into parts congruent to ±1 (mod 5) have their two-line matrix representation given in [7], where nice information was derived.…”