Asymptotics of parity biases for partitions into distinct parts via Nahm sums
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10489845" target="_blank" >RIV/00216208:11320/24:10489845 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Bj00dwM2jx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Bj00dwM2jx</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/plms.70010" target="_blank" >10.1112/plms.70010</a>
Alternative languages
Result language
angličtina
Original language name
Asymptotics of parity biases for partitions into distinct parts via Nahm sums
Original language description
For a random partition, one of the most basic questions is: what can one expect about the parts that arise? For example, what is the distribution of the parts of random partitions modulo N$N$? As most partitions contain a 1, and indeed many 1s arise as parts of a random partition, it is natural to expect a skew toward 1(modN)$1 (mathrm{mod} , N)$. This is indeed the case. For instance, Kim, Kim, and Lovejoy recently established "parity biases" showing how often one expects partitions to have more odd than even parts. Here, we generalize their work to give asymptotics for biases (modN)$ (mathrm{mod} , N)$ for partitions into distinct parts. The proofs rely on the Circle Method and give independently useful techniques for analyzing the asymptotics of Nahm-type q$q$-hypergeometric series.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the London Mathematical Society
ISSN
0024-6115
e-ISSN
1460-244X
Volume of the periodical
129
Issue of the periodical within the volume
6
Country of publishing house
GB - UNITED KINGDOM
Number of pages
40
Pages from-to
e70010
UT code for WoS article
001373492100005
EID of the result in the Scopus database
2-s2.0-85210068656