The Ramanujan Journal

, Volume 23, Issue 1–3, pp 159–167 | Cite as

On the subpartitions of the ordinary partitions



Let a 1a 2≥⋅⋅⋅≥a be an ordinary partition. A subpartition with gap d of an ordinary partition is defined as the longest sequence satisfying a 1>a 2>⋅⋅⋅>a s and a s >a s+1, where a i a j d for all i<js. This is a generalization of the Rogers–Ramanujan subpartition which was introduced by L. Kolitsch. In this note, we will study various properties of subpartitions, and as an application we will give a combinatorial proof of two entries which are in Ramanujan’s lost notebook.


Partition Subpartition Partial theta function 

Mathematics Subject Classification (2000)

11P81 05A17 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA

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