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Symmetric Identities from an Invariant in Partition Conjugation and Their Applications in q-Series

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DOI: 10.4236/ojdm.2014.42006    4,308 Downloads   5,499 Views  

ABSTRACT

For every partition and its conjugation , there is an important invariant , which denotes the number of different parts. That is , . We will derive a series of symmetric q-identities from the invariant in partition conjugation by studying modified Durfee rectangles. The extensive applications of the several symmetric q-identities in q-series  [1] will also be discussed. Without too much effort one can obtain much well-known knowledge as well as new formulas by proper substitutions and elementary calculations, such as symmetric identities, mock theta functions, a two-variable reciprocity theorem, identities from Ramanujan’s Lost Notebook and so on.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Chen, S. (2014) Symmetric Identities from an Invariant in Partition Conjugation and Their Applications in q-Series. Open Journal of Discrete Mathematics, 4, 36-43. doi: 10.4236/ojdm.2014.42006.

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