Atiyah-Sutcliffe Conjectures for Almost Collinear Configurations and Some New Conjectures for Symmetric Functions

In 2001 Sir M. F. Atiyah formulated a conjecture (C1) and later with P. Sutcliffe two stronger conjectures (C2) and (C3). These conjectures, inspired by physics (spin-statistics theorem of quantum mechanics), are geometrically defined for any configuration of points in the Euclidean three space. The...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Svrtan, Dragutin, Urbiha, Igor
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Svrtan, Dragutin
Urbiha, Igor
description In 2001 Sir M. F. Atiyah formulated a conjecture (C1) and later with P. Sutcliffe two stronger conjectures (C2) and (C3). These conjectures, inspired by physics (spin-statistics theorem of quantum mechanics), are geometrically defined for any configuration of points in the Euclidean three space. The conjecture (C1) is proved for n=3,4 and for general n only for some special configurations (M. F. Atiyah, M. Eastwood and P. Norbury, D. Djokovic). In this paper we shall explain some new conjectures for symmetric functions which imply (C2) and (C3) for almost collinear configurations. Computations up to n=6 are performed with a help of Maple and J. Stembridge's package SF for symmetric functions. For n=4 the conjectures (C2) and (C3) we have also verified for some infinite families of tetrahedra. This is a joint work with I. Urbiha. Finally we mention that by minimizing a geometrically defined energy, figuring in these conjectures, one gets a connection to some complicated physical theories, such as Skyrmions and Fullerenes.
doi_str_mv 10.48550/arxiv.math/0406386
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_math_0406386</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>math_0406386</sourcerecordid><originalsourceid>FETCH-LOGICAL-a716-98a3f319dd91efed8bac590a06e6dd9ba401a0d133daac7cbe3331fadb0b18813</originalsourceid><addsrcrecordid>eNplj7FOwzAURb0woMIXsJgPSGvLSeqMUUQBqYIh3aMX-7l1FdvgOED-nrZ0Y7rS1T1XOoQ8cLbMZVGwFcQf-7V0kA4rlrNSyPKWfNbJznDI2impwRqDtAn-iCpNEUdqQqT14MKYTvUwWI8QzwNj91OEZIMfKXhN2-CQvuH3P7idncMUraKbyasLcEduDAwj3l9zQXabp13zkm3fn1-bepvBmpdZJUEYwSutK44GtexBFRUDVmJ56nrIGQemuRAaQK1Vj0IIbkD3rOdScrEgj3-3F-vuI1oHce7O9t3VXvwCQG1aPQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Atiyah-Sutcliffe Conjectures for Almost Collinear Configurations and Some New Conjectures for Symmetric Functions</title><source>arXiv.org</source><creator>Svrtan, Dragutin ; Urbiha, Igor</creator><creatorcontrib>Svrtan, Dragutin ; Urbiha, Igor</creatorcontrib><description>In 2001 Sir M. F. Atiyah formulated a conjecture (C1) and later with P. Sutcliffe two stronger conjectures (C2) and (C3). These conjectures, inspired by physics (spin-statistics theorem of quantum mechanics), are geometrically defined for any configuration of points in the Euclidean three space. The conjecture (C1) is proved for n=3,4 and for general n only for some special configurations (M. F. Atiyah, M. Eastwood and P. Norbury, D. Djokovic). In this paper we shall explain some new conjectures for symmetric functions which imply (C2) and (C3) for almost collinear configurations. Computations up to n=6 are performed with a help of Maple and J. Stembridge's package SF for symmetric functions. For n=4 the conjectures (C2) and (C3) we have also verified for some infinite families of tetrahedra. This is a joint work with I. Urbiha. Finally we mention that by minimizing a geometrically defined energy, figuring in these conjectures, one gets a connection to some complicated physical theories, such as Skyrmions and Fullerenes.</description><identifier>DOI: 10.48550/arxiv.math/0406386</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2004-06</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/math/0406386$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.math/0406386$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Svrtan, Dragutin</creatorcontrib><creatorcontrib>Urbiha, Igor</creatorcontrib><title>Atiyah-Sutcliffe Conjectures for Almost Collinear Configurations and Some New Conjectures for Symmetric Functions</title><description>In 2001 Sir M. F. Atiyah formulated a conjecture (C1) and later with P. Sutcliffe two stronger conjectures (C2) and (C3). These conjectures, inspired by physics (spin-statistics theorem of quantum mechanics), are geometrically defined for any configuration of points in the Euclidean three space. The conjecture (C1) is proved for n=3,4 and for general n only for some special configurations (M. F. Atiyah, M. Eastwood and P. Norbury, D. Djokovic). In this paper we shall explain some new conjectures for symmetric functions which imply (C2) and (C3) for almost collinear configurations. Computations up to n=6 are performed with a help of Maple and J. Stembridge's package SF for symmetric functions. For n=4 the conjectures (C2) and (C3) we have also verified for some infinite families of tetrahedra. This is a joint work with I. Urbiha. Finally we mention that by minimizing a geometrically defined energy, figuring in these conjectures, one gets a connection to some complicated physical theories, such as Skyrmions and Fullerenes.</description><subject>Mathematics - Algebraic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2004</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNplj7FOwzAURb0woMIXsJgPSGvLSeqMUUQBqYIh3aMX-7l1FdvgOED-nrZ0Y7rS1T1XOoQ8cLbMZVGwFcQf-7V0kA4rlrNSyPKWfNbJznDI2impwRqDtAn-iCpNEUdqQqT14MKYTvUwWI8QzwNj91OEZIMfKXhN2-CQvuH3P7idncMUraKbyasLcEduDAwj3l9zQXabp13zkm3fn1-bepvBmpdZJUEYwSutK44GtexBFRUDVmJ56nrIGQemuRAaQK1Vj0IIbkD3rOdScrEgj3-3F-vuI1oHce7O9t3VXvwCQG1aPQ</recordid><startdate>20040619</startdate><enddate>20040619</enddate><creator>Svrtan, Dragutin</creator><creator>Urbiha, Igor</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20040619</creationdate><title>Atiyah-Sutcliffe Conjectures for Almost Collinear Configurations and Some New Conjectures for Symmetric Functions</title><author>Svrtan, Dragutin ; Urbiha, Igor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a716-98a3f319dd91efed8bac590a06e6dd9ba401a0d133daac7cbe3331fadb0b18813</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2004</creationdate><topic>Mathematics - Algebraic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Svrtan, Dragutin</creatorcontrib><creatorcontrib>Urbiha, Igor</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Svrtan, Dragutin</au><au>Urbiha, Igor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Atiyah-Sutcliffe Conjectures for Almost Collinear Configurations and Some New Conjectures for Symmetric Functions</atitle><date>2004-06-19</date><risdate>2004</risdate><abstract>In 2001 Sir M. F. Atiyah formulated a conjecture (C1) and later with P. Sutcliffe two stronger conjectures (C2) and (C3). These conjectures, inspired by physics (spin-statistics theorem of quantum mechanics), are geometrically defined for any configuration of points in the Euclidean three space. The conjecture (C1) is proved for n=3,4 and for general n only for some special configurations (M. F. Atiyah, M. Eastwood and P. Norbury, D. Djokovic). In this paper we shall explain some new conjectures for symmetric functions which imply (C2) and (C3) for almost collinear configurations. Computations up to n=6 are performed with a help of Maple and J. Stembridge's package SF for symmetric functions. For n=4 the conjectures (C2) and (C3) we have also verified for some infinite families of tetrahedra. This is a joint work with I. Urbiha. Finally we mention that by minimizing a geometrically defined energy, figuring in these conjectures, one gets a connection to some complicated physical theories, such as Skyrmions and Fullerenes.</abstract><doi>10.48550/arxiv.math/0406386</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.math/0406386
ispartof
issn
language eng
recordid cdi_arxiv_primary_math_0406386
source arXiv.org
subjects Mathematics - Algebraic Geometry
title Atiyah-Sutcliffe Conjectures for Almost Collinear Configurations and Some New Conjectures for Symmetric Functions
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-16T14%3A12%3A34IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Atiyah-Sutcliffe%20Conjectures%20for%20Almost%20Collinear%20Configurations%20and%20Some%20New%20Conjectures%20for%20Symmetric%20Functions&rft.au=Svrtan,%20Dragutin&rft.date=2004-06-19&rft_id=info:doi/10.48550/arxiv.math/0406386&rft_dat=%3Carxiv_GOX%3Emath_0406386%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true