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

Sandy H. L. Chen^{*}

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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.

References

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http://dx.doi.org/10.2307/2321943