Double series representations for Schur's partition function and related identities

作者：Andrews George^*; Bringmann Kathrin; Mahlburg Karl

来源：Journal of Combinatorial Theory - Series A, 2015, 132: 102-119.

DOI：10.1016/j.jcta.2014.12.004

• Partition
• q-series
• q-hypergeometric functions

We prove new double summation hypergeometric q-series representations for several families of partitions, including those that appear in the famous product identities of Gollnitz, Gordon, and Schur. We give several different proofs for our results, using bijective partitions mappings and modular diagrams, the theory of q-difference equations and recurrences, and the theories of summation and transformation for q-series. We also consider a general family of similar double series and highlight a number of other interesting special cases.

• 出版日期2015-5