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

DOI: 10.4236/ojdm.2014.42006   PDF   HTML     4,388 Downloads   5,627 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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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