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Parity bias for the partitions with bounded number of appearances of the part of size 1

Title
Parity bias for the partitions with bounded number of appearances of the part of size 1
Authors
KimByungchanEunmi
Ewha Authors
김은미
SCOPUS Author ID
김은미scopus
Issue Date
2024
Journal Title
Ramanujan Journal
ISSN
1382-4090JCR Link
Citation
Ramanujan Journal vol. 63, no. 3, pp. 657 - 671
Keywords
11P81Asymptotic formulaInteger partitionParity biasPartition injectionPrimary 05A17
Publisher
Springer
Indexed
SCIE; SCOPUS scopus
Document Type
Article
Abstract
While there are more partitions of n having more odd parts than even parts compared to partitions having more even parts than odd parts, we show that if there is a limit on the number of appearances of the part of size 1, there will eventually be more partitions of n with more even parts than odd parts compared to partitions with more odd parts than even parts. To demonstrate this, we obtain the asymptotic formulas for related partition functions via a Tauberian theorem, q-series manipulations, and partition combinatorics. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.
DOI
10.1007/s11139-023-00775-5
Appears in Collections:
연구기관 > 수리과학연구소 > Journal papers
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