TY - JOUR
T1 - Double series representations for Schur's partition function and related identities
AU - Andrews, George
AU - Bringmann, Kathrin
AU - Mahlburg, Karl
N1 - Funding Information:
The first author was partially supported by NSA grant H98230-12-1-0205 . The research of the second author was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation and the research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme ( FP/2007-2013 )/ ERC Grant agreement No. 335220 – AQSER. The third author was supported by NSF Grant DMS-1201435 .
Publisher Copyright:
© 2014.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - We prove new double summation hypergeometric q-series representations for several families of partitions, including those that appear in the famous product identities of Göllnitz, 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.
AB - We prove new double summation hypergeometric q-series representations for several families of partitions, including those that appear in the famous product identities of Göllnitz, 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.
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U2 - 10.1016/j.jcta.2014.12.004
DO - 10.1016/j.jcta.2014.12.004
M3 - Article
AN - SCOPUS:84920171358
SN - 0097-3165
VL - 132
SP - 102
EP - 119
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
ER -