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Annals of Combinatorics

, Volume 23, Issue 3–4, pp 835–888 | Cite as

Andrews–Gordon Type Series for Kanade–Russell Conjectures

  • Kağan KurşungözEmail author
Article
  • 17 Downloads

Abstract

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.

Keywords

Partition generating function Andrews–Gordon identities Kanade–Russell conjectures 

Mathematics Subject Classification

05A17 05A15 11P84 

Notes

Acknowledgements

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabancı UniversityİstanbulTurkey

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