TITLE:
Symmetric Identities from an Invariant in Partition Conjugation and Their Applications in q-Series
AUTHORS:
Sandy H. L. Chen
KEYWORDS:
Integer Partitions, Conjugation, Invariant, -Series, Symmetric Identities
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.4 No.2,
April
15,
2014
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.