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EnglishIn the work of Alladi et al. (J Algebra 174:636–658, 1995) the authors provided a generalization of the two Capparelli identities involving certain classes of integer partitions. Inspired by that contribution, in particular as regards the general setting and the tools the authors employed, we obtain new partition identities by identifying further sets of partitions that can be explicitly put into a one-to-one correspondence by the method described in the 1995 paper. As a further result, although of a different nature, we obtain an analytical identity of Rogers–Ramanujan type, involving generating functions, for a class of partition identities already found in that paper and that generalize the first Capparelli identity and include it as a particular case. To achieve this, we apply the same strategy as Kanade and Russell did in a recent paper. This method relies on the use of jagged partitions that can be seen as a more general kind of integer partitions.
Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection / Capparelli, S.; Del Fra, A.; Mercuri, P.; Vietri, A.. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - :(published 4 november 2020)(2020).
| Titolo: | Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection | |
| Autori: | VIETRI, Andrea (Corresponding author) | |
| Data di pubblicazione: | 2020 | |
| Rivista: | ||
| Citazione: | Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection / Capparelli, S.; Del Fra, A.; Mercuri, P.; Vietri, A.. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - :(published 4 november 2020)(2020). | |
| Handle: | http://hdl.handle.net/11573/1458390 | |
| Appartiene alla tipologia: | 01a Articolo in rivista |
File allegati a questo prodotto
| File | Note | Tipologia | Licenza | |
|---|---|---|---|---|
| Capparelli_preprint_Some-partition_2020.pdf | Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review) | Tutti i diritti riservati (All rights reserved) | Open Access Visualizza/Apri | |
| Capparelli_Some-partition_2020.pdf | Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione) | Tutti i diritti riservati (All rights reserved) | Open Access Visualizza/Apri |
http://hdl.handle.net/11573/1458390
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