Andrews–Gordon Type Series for Kanade–Russell Conjectures
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We construct Andrews–Gordon type positive series as generating functions of partitions satisfying certain difference conditions in six conjectures by Kanade and Russell. Thus, we obtain q-series conjectures as companions to Kanade and Russell’s combinatorial conjectures. We construct generating functions for missing partition enumerants as well, without claiming new partition identities.
KeywordsPartition generating function Andrews–Gordon identities Kanade–Russell conjectures
Mathematics Subject Classification05A17 05A15 11P84
We thank George E. Andrews, Alexander Berkovich, Karl Mahlburg and Dennis Stanton for useful discussions, suggesting references or terminology during the preparation of the manuscript. The term prestidigitation and the story in the Appendix is due to the historian and my friend Emre Erol of Sabancı University. We also thank the anonymous referees for their time and their suggestions for improvements.
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