SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS

SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS

For a given integer $n$ and a set $ \mathcal{S} \subseteq \mathbb{N} $, denote by ${ R}_{h, \mathcal{S} }^{(1)} (n)$ the number of solutions of the equation $n= {s}_{{i}_{1} } + \cdots + {s}_{{i}_{h} } $, ${s}_{{i}_{j} } \in \mathcal{S} $, $j= 1, \ldots , h$. In this paper we determine all pairs $(...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Bulletin of the Australian Mathematical Society 2014-02, Vol.89 (1), p.97-111
Hauptverfasser: KISS, SÁNDOR Z., ROZGONYI, ESZTER, SÁNDOR, CSABA
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 111
container_issue 1
container_start_page 97
container_title Bulletin of the Australian Mathematical Society
container_volume 89
creator KISS, SÁNDOR Z.
ROZGONYI, ESZTER
SÁNDOR, CSABA
description For a given integer $n$ and a set $ \mathcal{S} \subseteq \mathbb{N} $, denote by ${ R}_{h, \mathcal{S} }^{(1)} (n)$ the number of solutions of the equation $n= {s}_{{i}_{1} } + \cdots + {s}_{{i}_{h} } $, ${s}_{{i}_{j} } \in \mathcal{S} $, $j= 1, \ldots , h$. In this paper we determine all pairs $( \mathcal{A} , \mathcal{B} )$, $ \mathcal{A} , \mathcal{B} \subseteq \mathbb{N} $, for which ${ R}_{3, \mathcal{A} }^{(1)} (n)= { R}_{3, \mathcal{B} }^{(1)} (n)$ from a certain point on. We discuss some related problems.
doi_str_mv 10.1017/S0004972713000518
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2786971974</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0004972713000518</cupid><sourcerecordid>2786971974</sourcerecordid><originalsourceid>FETCH-LOGICAL-c360t-1878ed5ea239c8b789ba544248a48f6c4aef2da2c3f2fe5e122a9aed514efdd53</originalsourceid><addsrcrecordid>eNp1kE9Lw0AQxRdRMFY_gLeA5-jO_slujiGmbSAm0qR4DJtkV1qsqZv24Ld3QwsexNO8Yd7vDTyE7gE_AgbxVGGMWSSIAOoUB3mBPBCcBxBSeom86RxM92t0M45bt3FOpIdYldaV_5bVSz_OX8qq9pMyK5LsOSsW_ip9XaVVWtRxnZWFP18XySSqW3Rl1Meo785zhtbztE6WQV4usiTOg46G-BCAFFL3XCtCo062Qkat4owRJhWTJuyY0ob0inTUEKO5BkJUpBwBTJu-53SGHk65ezt8HfV4aLbD0X66lw0RMowERII5F5xcnR3G0WrT7O1mp-x3A7iZymn-lOMYembUrrWb_l3_Rv9P_QAmj2DG</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2786971974</pqid></control><display><type>article</type><title>SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>Cambridge Journals</source><creator>KISS, SÁNDOR Z. ; ROZGONYI, ESZTER ; SÁNDOR, CSABA</creator><creatorcontrib>KISS, SÁNDOR Z. ; ROZGONYI, ESZTER ; SÁNDOR, CSABA</creatorcontrib><description>For a given integer $n$ and a set $ \mathcal{S} \subseteq \mathbb{N} $, denote by ${ R}_{h, \mathcal{S} }^{(1)} (n)$ the number of solutions of the equation $n= {s}_{{i}_{1} } + \cdots + {s}_{{i}_{h} } $, ${s}_{{i}_{j} } \in \mathcal{S} $, $j= 1, \ldots , h$. In this paper we determine all pairs $( \mathcal{A} , \mathcal{B} )$, $ \mathcal{A} , \mathcal{B} \subseteq \mathbb{N} $, for which ${ R}_{3, \mathcal{A} }^{(1)} (n)= { R}_{3, \mathcal{B} }^{(1)} (n)$ from a certain point on. We discuss some related problems.</description><identifier>ISSN: 0004-9727</identifier><identifier>EISSN: 1755-1633</identifier><identifier>DOI: 10.1017/S0004972713000518</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><ispartof>Bulletin of the Australian Mathematical Society, 2014-02, Vol.89 (1), p.97-111</ispartof><rights>Copyright ©2013 Australian Mathematical Publishing Association Inc.</rights><rights>Copyright ©2013 Australian Mathematical Publishing Association Inc.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-1878ed5ea239c8b789ba544248a48f6c4aef2da2c3f2fe5e122a9aed514efdd53</citedby><cites>FETCH-LOGICAL-c360t-1878ed5ea239c8b789ba544248a48f6c4aef2da2c3f2fe5e122a9aed514efdd53</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0004972713000518/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids></links><search><creatorcontrib>KISS, SÁNDOR Z.</creatorcontrib><creatorcontrib>ROZGONYI, ESZTER</creatorcontrib><creatorcontrib>SÁNDOR, CSABA</creatorcontrib><title>SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS</title><title>Bulletin of the Australian Mathematical Society</title><addtitle>Bull. Aust. Math. Soc</addtitle><description>For a given integer $n$ and a set $ \mathcal{S} \subseteq \mathbb{N} $, denote by ${ R}_{h, \mathcal{S} }^{(1)} (n)$ the number of solutions of the equation $n= {s}_{{i}_{1} } + \cdots + {s}_{{i}_{h} } $, ${s}_{{i}_{j} } \in \mathcal{S} $, $j= 1, \ldots , h$. In this paper we determine all pairs $( \mathcal{A} , \mathcal{B} )$, $ \mathcal{A} , \mathcal{B} \subseteq \mathbb{N} $, for which ${ R}_{3, \mathcal{A} }^{(1)} (n)= { R}_{3, \mathcal{B} }^{(1)} (n)$ from a certain point on. We discuss some related problems.</description><issn>0004-9727</issn><issn>1755-1633</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNp1kE9Lw0AQxRdRMFY_gLeA5-jO_slujiGmbSAm0qR4DJtkV1qsqZv24Ld3QwsexNO8Yd7vDTyE7gE_AgbxVGGMWSSIAOoUB3mBPBCcBxBSeom86RxM92t0M45bt3FOpIdYldaV_5bVSz_OX8qq9pMyK5LsOSsW_ip9XaVVWtRxnZWFP18XySSqW3Rl1Meo785zhtbztE6WQV4usiTOg46G-BCAFFL3XCtCo062Qkat4owRJhWTJuyY0ob0inTUEKO5BkJUpBwBTJu-53SGHk65ezt8HfV4aLbD0X66lw0RMowERII5F5xcnR3G0WrT7O1mp-x3A7iZymn-lOMYembUrrWb_l3_Rv9P_QAmj2DG</recordid><startdate>201402</startdate><enddate>201402</enddate><creator>KISS, SÁNDOR Z.</creator><creator>ROZGONYI, ESZTER</creator><creator>SÁNDOR, CSABA</creator><general>Cambridge University Press</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7XB</scope><scope>88I</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M2P</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>201402</creationdate><title>SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS</title><author>KISS, SÁNDOR Z. ; ROZGONYI, ESZTER ; SÁNDOR, CSABA</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-1878ed5ea239c8b789ba544248a48f6c4aef2da2c3f2fe5e122a9aed514efdd53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>KISS, SÁNDOR Z.</creatorcontrib><creatorcontrib>ROZGONYI, ESZTER</creatorcontrib><creatorcontrib>SÁNDOR, CSABA</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Bulletin of the Australian Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>KISS, SÁNDOR Z.</au><au>ROZGONYI, ESZTER</au><au>SÁNDOR, CSABA</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS</atitle><jtitle>Bulletin of the Australian Mathematical Society</jtitle><addtitle>Bull. Aust. Math. Soc</addtitle><date>2014-02</date><risdate>2014</risdate><volume>89</volume><issue>1</issue><spage>97</spage><epage>111</epage><pages>97-111</pages><issn>0004-9727</issn><eissn>1755-1633</eissn><abstract>For a given integer $n$ and a set $ \mathcal{S} \subseteq \mathbb{N} $, denote by ${ R}_{h, \mathcal{S} }^{(1)} (n)$ the number of solutions of the equation $n= {s}_{{i}_{1} } + \cdots + {s}_{{i}_{h} } $, ${s}_{{i}_{j} } \in \mathcal{S} $, $j= 1, \ldots , h$. In this paper we determine all pairs $( \mathcal{A} , \mathcal{B} )$, $ \mathcal{A} , \mathcal{B} \subseteq \mathbb{N} $, for which ${ R}_{3, \mathcal{A} }^{(1)} (n)= { R}_{3, \mathcal{B} }^{(1)} (n)$ from a certain point on. We discuss some related problems.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0004972713000518</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0004-9727
ispartof Bulletin of the Australian Mathematical Society, 2014-02, Vol.89 (1), p.97-111
issn 0004-9727
1755-1633
language eng
recordid cdi_proquest_journals_2786971974
source Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Cambridge Journals
title SETS WITH ALMOST COINCIDING REPRESENTATION FUNCTIONS
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T17%3A33%3A52IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=SETS%20WITH%20ALMOST%20COINCIDING%20REPRESENTATION%20FUNCTIONS&rft.jtitle=Bulletin%20of%20the%20Australian%20Mathematical%20Society&rft.au=KISS,%20S%C3%81NDOR%20Z.&rft.date=2014-02&rft.volume=89&rft.issue=1&rft.spage=97&rft.epage=111&rft.pages=97-111&rft.issn=0004-9727&rft.eissn=1755-1633&rft_id=info:doi/10.1017/S0004972713000518&rft_dat=%3Cproquest_cross%3E2786971974%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2786971974&rft_id=info:pmid/&rft_cupid=10_1017_S0004972713000518&rfr_iscdi=true