A Partition Identity Related to Stanley's Theorem

In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of \(1\)'s in the partitions of \(n\). A new expansion for Euler's partition function \(p(n)\) is derived in this context. These surprising new results...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:arXiv.org
Hlavní autori: Merca, Mircea, Schmidt, Maxie D
Médium: Paper
Jazyk:English
Vydavateľské údaje: Ithaca Cornell University Library, arXiv.org 20.10.2023
Predmet:
Number theory
Partitions (mathematics)
ISSN:2331-8422
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Abstract In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of \(1\)'s in the partitions of \(n\). A new expansion for Euler's partition function \(p(n)\) is derived in this context. These surprising new results connect the famous classical totient function from multiplicative number theory to the additive theory of partitions.
AbstractList In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of \(1\)'s in the partitions of \(n\). A new expansion for Euler's partition function \(p(n)\) is derived in this context. These surprising new results connect the famous classical totient function from multiplicative number theory to the additive theory of partitions.
Author Schmidt, Maxie D
Merca, Mircea
Author_xml – sequence: 1
  givenname: Mircea
  surname: Merca
  fullname: Merca, Mircea
– sequence: 2
  givenname: Maxie
  surname: Schmidt
  middlename: D
  fullname: Schmidt, Maxie D
BookMark eNotjVFLwzAUhYMoOOd-gG8BH3zqTG5ym-RxDJ2DgaJ9H7dNih010TYT9-8t6NM5fAe-c8XOY4qBsRspltoiinsafrrvJagJSFUaOGMzUEoWVgNcssU4HoQQMA2Iasbkir_QkLvcpci3PsSpnvhr6CkHz3Pib5liH053I6_eQxrCxzW7aKkfw-I_56x6fKjWT8XuebNdr3YFIbhCKiDZCqNRoUdFFm0NbeNqXTal16SM840GQyVgkOhMXcsykHU1WtM4r-bs9k_7OaSvYxjz_pCOQ5we92CtQAdOO_ULk8tF-w
ContentType Paper
Copyright 2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2023. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
DOI 10.48550/arxiv.2310.13672
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central
ProQuest Central UK/Ireland
ProQuest Central Essentials
ProQuest Central
ProQuest Technology Collection
ProQuest One
ProQuest Central Korea
SciTech Premium Collection (via ProQuest)
ProQuest Engineering Collection
Engineering Database
ProQuest Central Premium
ProQuest One Academic
ProQuest Publicly Available Content Database
ProQuest One Academic Middle East (New)
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Applied & Life Sciences
ProQuest One Academic (retired)
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest One Academic Middle East (New)
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest One Applied & Life Sciences
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest Central (New)
ProQuest One Academic
ProQuest One Academic (New)
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: PIMPY
  name: Publicly Available Content Database
  url: http://search.proquest.com/publiccontent
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PHGZM
PHGZT
PIMPY
PKEHL
PQEST
PQGLB
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-LOGICAL-a529-132a1f074535d53a858b2fc9b46c6d4a379dc427a625e1597bb16ea89b587c9d3
IEDL.DBID BENPR
IngestDate Mon Jun 30 09:17:05 EDT 2025
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-a529-132a1f074535d53a858b2fc9b46c6d4a379dc427a625e1597bb16ea89b587c9d3
Notes SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
OpenAccessLink https://www.proquest.com/docview/2880592949?pq-origsite=%requestingapplication%
PQID 2880592949
PQPubID 2050157
ParticipantIDs proquest_journals_2880592949
PublicationCentury 2000
PublicationDate 20231020
PublicationDateYYYYMMDD 2023-10-20
PublicationDate_xml – month: 10
  year: 2023
  text: 20231020
  day: 20
PublicationDecade 2020
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2023
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 1.8483672
SecondaryResourceType preprint
Snippet In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of \(1\)'s in the...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Number theory
Partitions (mathematics)
Title A Partition Identity Related to Stanley's Theorem
URI https://www.proquest.com/docview/2880592949
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV07T8MwED5BCxITb_EoVQYkJtPGseN4QoBawUAVQYcyVX5F6kBbklLBv-dsUhALC2NkRUrOp7vvzp_vAzinLuMZQgFSGJ4Sn_GIMqxLlCjSWAuJkMMGsQkxGGSjkczrhltV0ypXMTEEajszvkfeoehoHHM5k1fzV-JVo_zpai2hsQ5NP6mMNaB50xvkj99dFpoKxMzJ13FmGN7VUeX7ZHnpYY2neIXJwL-DcMgs_e3_ftMONHM1d-UurLnpHmwGRqep9iG-jnLvFt7wUX0d9yMK3Ddno8Us8vrBGBEuqijcz3cvBzDs94a3d6TWRyCKU0mwjlRxgRCAJ9zyRKHRNS2M1Cw1qWUqEdIaRoXCEschahFax6lTmdQ8E0ba5BAa09nUHUGENVNsZcGpsPh20dWGygwrMQQXTAmTHENrZYBx7ePV-OfvT_5ePoUtL9LuIz7ttqCxKN_cGWyY5WJSle16y9qedfmET_n9Q_78CZEJocM
linkProvider ProQuest
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V07T8MwED6VFgQTb_EokAHEFNo4cRwPCCGgatWHMnQoU-XYjtSBtiSl0B_Ff-ScJiAWtg7MUSLn_Pm-O_t8H8Al0QENMBSwY0l92zCeLaRXtwWLfSdiHEMOlYlNsF4vGAx4WILP4i6MKassfGLmqNVEmj3yGkGgUeRyj99NX22jGmVOVwsJjSUs2nrxjilbett6xPm9IqTx1H9o2rmqgC0o4TZmX8KJkTipSxV1BQ41IrHkkedLX3nCZVxJjzCBiYFGrmdR5PhaBDyiAZNcufjZNah4iPWgDJWw1Q2fvzd1iM8wRHeXp6dZr7CaSD5G8xsTRZmKsqwR8W-fnxFZY_ufmWAHf11MdbILJT3eg42sXlWm--DcW6EBvYGVlV82XlhZZZ9W1mxiGXVk9HfXqZV1H9AvB9BfxSAPoTyejPURWJgROorHlDCFb8f1SBIeYJ6JoZMnmHSPoVrYe5iv4HT4Y-yTvx9fwGaz3-0MO61e-xS2jBy94TZSr0J5lrzpM1iX89koTc5ztFgwXPHkfAEs1fmc
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+Partition+Identity+Related+to+Stanley%27s+Theorem&rft.jtitle=arXiv.org&rft.au=Merca%2C+Mircea&rft.au=Schmidt%2C+Maxie+D&rft.date=2023-10-20&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.2310.13672