Kurşungöz, Kağan and Ömrüuzun Seyrek, Halime (2022) Construction of evidently positive series and an alternative construction for a family of partition generating functions due to Kanade and Russell. Annals of Combinatorics . ISSN 0218-0006 (Print) 0219-3094 (Online) Published Online First https://dx.doi.org/10.1007/s00026-022-00597-0
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Official URL: https://dx.doi.org/10.1007/s00026-022-00597-0
Abstract
We give an alternative construction for a family of partition generating functions due to Kanade and Russell. In our alternative construction, we use ordinary partitions instead of jagged partitions. We also present new generating functions which are evidently positive series for partitions due to Kanade and Russell. To obtain those generating functions, we first construct an evidently positive series for a key infinite product. In that construction, a series of combinatorial moves is used to decompose an arbitrary partition into a base partition together with some auxiliary partitions that bijectively record the moves.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Evidently positive generating functions; Integer partition; Partition generating function; Rogers-Ramanujan type partition identities |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | Kağan Kurşungöz |
| Date Deposited: | 04 Sep 2022 18:24 |
| Last Modified: | 04 Sep 2022 18:24 |
| URI: | https://research.sabanciuniv.edu/id/eprint/44335 |
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- Construction of evidently positive series and an alternative construction for a family of partition generating functions due to Kanade and Russell. (deposited 04 Sep 2022 18:24) [Currently Displayed]
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