Publish in OALib Journal
APC: Only $99
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  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.