Magic sets for polynomials of degree n
Let Pn be the family of all real, non-constant polynomials with degree at most n and let Qn be the family of all complex, non-constant polynomials with degree at most n. A set S⊆R is called a set of range uniqueness (SRU) for a family F∈{Pn,Qn} if for all f,g∈F, f[S]=g[S]⇒f=g. And S is called a magi...
Gespeichert in:
| Veröffentlicht in: | Linear algebra and its applications 2021-01, Vol.609, p.413-441 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 441 |
|---|---|
| container_issue | |
| container_start_page | 413 |
| container_title | Linear algebra and its applications |
| container_volume | 609 |
| creator | Halbeisen, Lorenz Hungerbühler, Norbert Schumacher, Salome |
| description | Let Pn be the family of all real, non-constant polynomials with degree at most n and let Qn be the family of all complex, non-constant polynomials with degree at most n. A set S⊆R is called a set of range uniqueness (SRU) for a family F∈{Pn,Qn} if for all f,g∈F, f[S]=g[S]⇒f=g. And S is called a magic set if for all f,g∈F, f[S]⊆g[S]⇒f=g. In this paper we will show that there are magic sets for Pn and Qn of size s for every s≥2n+1. However, there are no SRUs of size at most 2n for Pn and Qn. Moreover we will show that SRUs and magic sets are not the same by giving examples of SRUs for P2 and P3 that are not magic. |
| doi_str_mv | 10.1016/j.laa.2020.09.026 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_elsev</sourceid><recordid>TN_cdi_proquest_journals_2488017821</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0024379520304481</els_id><sourcerecordid>2488017821</sourcerecordid><originalsourceid>FETCH-LOGICAL-c368t-b1c022a65c1de9bd52d86ae9b02b59d41f1f3d028692161b959310a1f9cb6cf13</originalsourceid><addsrcrecordid>eNqNkE1LAzEQhoMoWKs_wNuC4EV2ncl2swmepPgFFS96DtlsUrK0m5pslf57U7Z4FE8zDO8zMzyEXCIUCMhuu2KlVEGBQgGiAMqOyAR5XebIK3ZMJgB0lpe1qE7JWYwdAMxqoBNy_aqWTmfRDDGzPmQbv9r1fu3UKmbeZq1ZBmOy_pyc2DQyF4c6JR-PD-_z53zx9vQyv1_kumR8yBvUQKlilcbWiKataMuZSh3QphLtDC3asgXKmaDIsBGVKBEUWqEbpi2WU3I17t0E_7k1cZCd34Y-nZR0xjlgzek-hWNKBx9jMFZuglursJMIcq9DdjLpkHsdEoRMOhLDR-bbNN5G7UyvzS-XfFQc6xKq1FE6d4ManO_nftsPCb35P5rSd2PaJE9fzgR5IFoXjB5k690fb_4AdQuGFQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2488017821</pqid></control><display><type>article</type><title>Magic sets for polynomials of degree n</title><source>Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" /></source><source>Access via ScienceDirect (Elsevier)</source><creator>Halbeisen, Lorenz ; Hungerbühler, Norbert ; Schumacher, Salome</creator><creatorcontrib>Halbeisen, Lorenz ; Hungerbühler, Norbert ; Schumacher, Salome</creatorcontrib><description>Let Pn be the family of all real, non-constant polynomials with degree at most n and let Qn be the family of all complex, non-constant polynomials with degree at most n. A set S⊆R is called a set of range uniqueness (SRU) for a family F∈{Pn,Qn} if for all f,g∈F, f[S]=g[S]⇒f=g. And S is called a magic set if for all f,g∈F, f[S]⊆g[S]⇒f=g. In this paper we will show that there are magic sets for Pn and Qn of size s for every s≥2n+1. However, there are no SRUs of size at most 2n for Pn and Qn. Moreover we will show that SRUs and magic sets are not the same by giving examples of SRUs for P2 and P3 that are not magic.</description><identifier>ISSN: 0024-3795</identifier><identifier>EISSN: 1873-1856</identifier><identifier>DOI: 10.1016/j.laa.2020.09.026</identifier><language>eng</language><publisher>NEW YORK: Elsevier Inc</publisher><subject>Linear algebra ; Magic sets ; Mathematics ; Mathematics, Applied ; Physical Sciences ; Polynomials ; Science & Technology ; Sets of range uniqueness ; Unique range</subject><ispartof>Linear algebra and its applications, 2021-01, Vol.609, p.413-441</ispartof><rights>2020 The Authors</rights><rights>Copyright American Elsevier Company, Inc. Jan 15, 2021</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>2</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000581730500022</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c368t-b1c022a65c1de9bd52d86ae9b02b59d41f1f3d028692161b959310a1f9cb6cf13</citedby><cites>FETCH-LOGICAL-c368t-b1c022a65c1de9bd52d86ae9b02b59d41f1f3d028692161b959310a1f9cb6cf13</cites><orcidid>0000-0001-6191-0022 ; 0000-0001-6078-7237</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.laa.2020.09.026$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>315,781,785,3551,27928,27929,39262,45999</link.rule.ids></links><search><creatorcontrib>Halbeisen, Lorenz</creatorcontrib><creatorcontrib>Hungerbühler, Norbert</creatorcontrib><creatorcontrib>Schumacher, Salome</creatorcontrib><title>Magic sets for polynomials of degree n</title><title>Linear algebra and its applications</title><addtitle>LINEAR ALGEBRA APPL</addtitle><description>Let Pn be the family of all real, non-constant polynomials with degree at most n and let Qn be the family of all complex, non-constant polynomials with degree at most n. A set S⊆R is called a set of range uniqueness (SRU) for a family F∈{Pn,Qn} if for all f,g∈F, f[S]=g[S]⇒f=g. And S is called a magic set if for all f,g∈F, f[S]⊆g[S]⇒f=g. In this paper we will show that there are magic sets for Pn and Qn of size s for every s≥2n+1. However, there are no SRUs of size at most 2n for Pn and Qn. Moreover we will show that SRUs and magic sets are not the same by giving examples of SRUs for P2 and P3 that are not magic.</description><subject>Linear algebra</subject><subject>Magic sets</subject><subject>Mathematics</subject><subject>Mathematics, Applied</subject><subject>Physical Sciences</subject><subject>Polynomials</subject><subject>Science & Technology</subject><subject>Sets of range uniqueness</subject><subject>Unique range</subject><issn>0024-3795</issn><issn>1873-1856</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>HGBXW</sourceid><recordid>eNqNkE1LAzEQhoMoWKs_wNuC4EV2ncl2swmepPgFFS96DtlsUrK0m5pslf57U7Z4FE8zDO8zMzyEXCIUCMhuu2KlVEGBQgGiAMqOyAR5XebIK3ZMJgB0lpe1qE7JWYwdAMxqoBNy_aqWTmfRDDGzPmQbv9r1fu3UKmbeZq1ZBmOy_pyc2DQyF4c6JR-PD-_z53zx9vQyv1_kumR8yBvUQKlilcbWiKataMuZSh3QphLtDC3asgXKmaDIsBGVKBEUWqEbpi2WU3I17t0E_7k1cZCd34Y-nZR0xjlgzek-hWNKBx9jMFZuglursJMIcq9DdjLpkHsdEoRMOhLDR-bbNN5G7UyvzS-XfFQc6xKq1FE6d4ManO_nftsPCb35P5rSd2PaJE9fzgR5IFoXjB5k690fb_4AdQuGFQ</recordid><startdate>20210115</startdate><enddate>20210115</enddate><creator>Halbeisen, Lorenz</creator><creator>Hungerbühler, Norbert</creator><creator>Schumacher, Salome</creator><general>Elsevier Inc</general><general>Elsevier</general><general>American Elsevier Company, Inc</general><scope>6I.</scope><scope>AAFTH</scope><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-6191-0022</orcidid><orcidid>https://orcid.org/0000-0001-6078-7237</orcidid></search><sort><creationdate>20210115</creationdate><title>Magic sets for polynomials of degree n</title><author>Halbeisen, Lorenz ; Hungerbühler, Norbert ; Schumacher, Salome</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368t-b1c022a65c1de9bd52d86ae9b02b59d41f1f3d028692161b959310a1f9cb6cf13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Linear algebra</topic><topic>Magic sets</topic><topic>Mathematics</topic><topic>Mathematics, Applied</topic><topic>Physical Sciences</topic><topic>Polynomials</topic><topic>Science & Technology</topic><topic>Sets of range uniqueness</topic><topic>Unique range</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Halbeisen, Lorenz</creatorcontrib><creatorcontrib>Hungerbühler, Norbert</creatorcontrib><creatorcontrib>Schumacher, Salome</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Linear algebra and its applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Halbeisen, Lorenz</au><au>Hungerbühler, Norbert</au><au>Schumacher, Salome</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Magic sets for polynomials of degree n</atitle><jtitle>Linear algebra and its applications</jtitle><stitle>LINEAR ALGEBRA APPL</stitle><date>2021-01-15</date><risdate>2021</risdate><volume>609</volume><spage>413</spage><epage>441</epage><pages>413-441</pages><issn>0024-3795</issn><eissn>1873-1856</eissn><abstract>Let Pn be the family of all real, non-constant polynomials with degree at most n and let Qn be the family of all complex, non-constant polynomials with degree at most n. A set S⊆R is called a set of range uniqueness (SRU) for a family F∈{Pn,Qn} if for all f,g∈F, f[S]=g[S]⇒f=g. And S is called a magic set if for all f,g∈F, f[S]⊆g[S]⇒f=g. In this paper we will show that there are magic sets for Pn and Qn of size s for every s≥2n+1. However, there are no SRUs of size at most 2n for Pn and Qn. Moreover we will show that SRUs and magic sets are not the same by giving examples of SRUs for P2 and P3 that are not magic.</abstract><cop>NEW YORK</cop><pub>Elsevier Inc</pub><doi>10.1016/j.laa.2020.09.026</doi><tpages>29</tpages><orcidid>https://orcid.org/0000-0001-6191-0022</orcidid><orcidid>https://orcid.org/0000-0001-6078-7237</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0024-3795 |
| ispartof | Linear algebra and its applications, 2021-01, Vol.609, p.413-441 |
| issn | 0024-3795 1873-1856 |
| language | eng |
| recordid | cdi_proquest_journals_2488017821 |
| source | Web of Science - Science Citation Index Expanded - 2021<img src="https://exlibris-pub.s3.amazonaws.com/fromwos-v2.jpg" />; Access via ScienceDirect (Elsevier) |
| subjects | Linear algebra Magic sets Mathematics Mathematics, Applied Physical Sciences Polynomials Science & Technology Sets of range uniqueness Unique range |
| title | Magic sets for polynomials of degree n |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-16T20%3A18%3A49IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_elsev&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Magic%20sets%20for%20polynomials%20of%20degree%20n&rft.jtitle=Linear%20algebra%20and%20its%20applications&rft.au=Halbeisen,%20Lorenz&rft.date=2021-01-15&rft.volume=609&rft.spage=413&rft.epage=441&rft.pages=413-441&rft.issn=0024-3795&rft.eissn=1873-1856&rft_id=info:doi/10.1016/j.laa.2020.09.026&rft_dat=%3Cproquest_elsev%3E2488017821%3C/proquest_elsev%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2488017821&rft_id=info:pmid/&rft_els_id=S0024379520304481&rfr_iscdi=true |