Symmetric Identities from an Invariant in Partition Conjugation and Their Applications in <i>q</i>-Series

• 作者: Sandy H. L. Chen
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: Integer Partitions CONJUGATION INVARIANT -Series SYMMETRIC IDENTITIES
• 年，卷（期）: 2014,（2）
• 页码范围: 36-43
• 页数: 8页
• 分类号: O1

摘要

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.