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

Abstract

In this work we talk about some patterns on partitions considered by the 1st 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.