On the number of equivalence classes arising from partition involutions. II
type: Item
instance of: scholarly article
title: On the number of equivalence classes arising from partition involutions. II
zbMATH Open document ID: 1473.11189
author: Byungchan Kim
author: JiSun Huh
published in: Discrete Mathematics
publication date: 2021-06-14T00:00:00Z
review text: The authors investigated partition identities while considering classical involutions related with Crank of partitions; and established few new identities relating the number of equivalence classes under the involution and the numbers of partitions satisfying a certain parity condition. Further, authors proved two new fundamental results, as (i). If \(\phi\) be the involution on the set of Frobenius symbol representations of partitions with odd parts distinct, then, for all positive integers \(n\), \(P^{\phi}_{o}(n)=pod_{3}(n)\), where \(pod_{3}(n)\) is the number of partitions with odd parts distinct satisfying that the total number of parts \(\equiv 0 \pmod 3\) is even; and (ii). For a positive integer \(k\), let \(\phi\) be the involution on the set of \(k\)-colored generalized Frobenius partitions, defined by switching the rows, for all positive integers \(n\), \(F^{\phi}_{\overline{C}_{k}, \overline{C}_{k}} (n)=F^{m}_{k}(n)\), where \(F^{m}_{k}(n)\) is the number of \(k\)-colored \(F\)-partitions satisfying that \(m_{F} (\pi) \equiv n + k-1\pmod 2\). The results presented in this article are new, interesting and useful for the researchers. For Part I see [the authors, Int. J. Number Theory 16, No. 5, 925--939 (2020; Zbl 1440.05032)].
reviewed by: M. P. Chaudhary
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 05A17
Mathematics Subject Classification ID: 11P83
zbMATH DE Number: 7358333
zbMATH Keywords: partition involutions
zbMATH Keywords: pseudo-conjugation
zbMATH Keywords: parity
zbMATH Keywords: equivalence class
MaRDI profile type: Publication
full work available at URL: j.disc.2021.112410
OpenAlex ID: W3151028859
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DOI: 10.1016/J.DISC.2021.112410
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description: scientific article; zbMATH DE number 7358333