Hypergraph LSS-ideals and coordinate sections of symmetric tensors
Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an integer d >= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the polynomials $f^{(d)}_{e}= \sum\limits_{j=1}^{d} \prod\limits_{i \in e} y_{ij}$ for edges e o...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| 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 | Gharakhloo, Shekoofeh Welker, Volkmar |
| description | Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an
integer d >= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in
K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the polynomials
$f^{(d)}_{e}= \sum\limits_{j=1}^{d} \prod\limits_{i \in e} y_{ij}$ for edges e
of H. In this paper for an algebraically closed field K and a k-uniform
hypergraph H=([n],E) we employ a connection between LSS-ideals and coordinate
sections of the closure of the set S_{n,k}^d of homogeneous degree k symmetric
tensors in n variables of rank |
| doi_str_mv | 10.48550/arxiv.2202.10463 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2202_10463</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2202_10463</sourcerecordid><originalsourceid>FETCH-LOGICAL-a673-16b68af7eafa72a018a8f71dc1fa3c62320563ced75c086fbfd48fe27759a0b43</originalsourceid><addsrcrecordid>eNotz71OwzAYhWEvHVDLBTDVN5DUP_EPI62AIkXq0O7RF_tzsUTiyI4QuXugMJ3pPdJDyANndWOVYjvIX_GzFoKJmrNGyzuyPy4T5muG6Z2253MVPcJHoTB66lLKPo4wIy3o5pjGQlOgZRkGnHN0dMaxpFw2ZBV-Grz_3zW5vDxfDseqPb2-HZ7aCrSRFde9thAMQgAjgHELNhjuHQ8gnRZSMKWlQ2-UY1aHPvjGBhTGqEdgfSPXZPt3e0N0U44D5KX7xXQ3jPwGByNFTw</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Hypergraph LSS-ideals and coordinate sections of symmetric tensors</title><source>arXiv.org</source><creator>Gharakhloo, Shekoofeh ; Welker, Volkmar</creator><creatorcontrib>Gharakhloo, Shekoofeh ; Welker, Volkmar</creatorcontrib><description>Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an
integer d >= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in
K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the polynomials
$f^{(d)}_{e}= \sum\limits_{j=1}^{d} \prod\limits_{i \in e} y_{ij}$ for edges e
of H. In this paper for an algebraically closed field K and a k-uniform
hypergraph H=([n],E) we employ a connection between LSS-ideals and coordinate
sections of the closure of the set S_{n,k}^d of homogeneous degree k symmetric
tensors in n variables of rank <= d to derive results on the irreducibility of
its coordinate sections. To this end we provide results on primality and the
complete intersection property of L_H^K (d). We then use the combinatorial
concept of positive matching decomposition of a hypergraph H to provide bounds
on when L_H^K(d) turns prime to provide results on the irreducibility of
coordinate sections of S_{n, k}^d.</description><identifier>DOI: 10.48550/arxiv.2202.10463</identifier><language>eng</language><subject>Mathematics - Combinatorics ; Mathematics - Commutative Algebra</subject><creationdate>2022-02</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2202.10463$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2202.10463$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Gharakhloo, Shekoofeh</creatorcontrib><creatorcontrib>Welker, Volkmar</creatorcontrib><title>Hypergraph LSS-ideals and coordinate sections of symmetric tensors</title><description>Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an
integer d >= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in
K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the polynomials
$f^{(d)}_{e}= \sum\limits_{j=1}^{d} \prod\limits_{i \in e} y_{ij}$ for edges e
of H. In this paper for an algebraically closed field K and a k-uniform
hypergraph H=([n],E) we employ a connection between LSS-ideals and coordinate
sections of the closure of the set S_{n,k}^d of homogeneous degree k symmetric
tensors in n variables of rank <= d to derive results on the irreducibility of
its coordinate sections. To this end we provide results on primality and the
complete intersection property of L_H^K (d). We then use the combinatorial
concept of positive matching decomposition of a hypergraph H to provide bounds
on when L_H^K(d) turns prime to provide results on the irreducibility of
coordinate sections of S_{n, k}^d.</description><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Commutative Algebra</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz71OwzAYhWEvHVDLBTDVN5DUP_EPI62AIkXq0O7RF_tzsUTiyI4QuXugMJ3pPdJDyANndWOVYjvIX_GzFoKJmrNGyzuyPy4T5muG6Z2253MVPcJHoTB66lLKPo4wIy3o5pjGQlOgZRkGnHN0dMaxpFw2ZBV-Grz_3zW5vDxfDseqPb2-HZ7aCrSRFde9thAMQgAjgHELNhjuHQ8gnRZSMKWlQ2-UY1aHPvjGBhTGqEdgfSPXZPt3e0N0U44D5KX7xXQ3jPwGByNFTw</recordid><startdate>20220221</startdate><enddate>20220221</enddate><creator>Gharakhloo, Shekoofeh</creator><creator>Welker, Volkmar</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20220221</creationdate><title>Hypergraph LSS-ideals and coordinate sections of symmetric tensors</title><author>Gharakhloo, Shekoofeh ; Welker, Volkmar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-16b68af7eafa72a018a8f71dc1fa3c62320563ced75c086fbfd48fe27759a0b43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Commutative Algebra</topic><toplevel>online_resources</toplevel><creatorcontrib>Gharakhloo, Shekoofeh</creatorcontrib><creatorcontrib>Welker, Volkmar</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Gharakhloo, Shekoofeh</au><au>Welker, Volkmar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hypergraph LSS-ideals and coordinate sections of symmetric tensors</atitle><date>2022-02-21</date><risdate>2022</risdate><abstract>Let K be a field, [n]= {1,...,n} and H=([n],E) be a hypergraph. For an
integer d >= 1 the Lovasz-Saks-Schrijver ideal (LSS-ideal) L_H^K (d) in
K[y_{ij}~:~(i,j) \in [n] x [d]] is the ideal generated by the polynomials
$f^{(d)}_{e}= \sum\limits_{j=1}^{d} \prod\limits_{i \in e} y_{ij}$ for edges e
of H. In this paper for an algebraically closed field K and a k-uniform
hypergraph H=([n],E) we employ a connection between LSS-ideals and coordinate
sections of the closure of the set S_{n,k}^d of homogeneous degree k symmetric
tensors in n variables of rank <= d to derive results on the irreducibility of
its coordinate sections. To this end we provide results on primality and the
complete intersection property of L_H^K (d). We then use the combinatorial
concept of positive matching decomposition of a hypergraph H to provide bounds
on when L_H^K(d) turns prime to provide results on the irreducibility of
coordinate sections of S_{n, k}^d.</abstract><doi>10.48550/arxiv.2202.10463</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2202.10463 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2202_10463 |
| source | arXiv.org |
| subjects | Mathematics - Combinatorics Mathematics - Commutative Algebra |
| title | Hypergraph LSS-ideals and coordinate sections of symmetric tensors |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T01%3A44%3A58IST&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=Hypergraph%20LSS-ideals%20and%20coordinate%20sections%20of%20symmetric%20tensors&rft.au=Gharakhloo,%20Shekoofeh&rft.date=2022-02-21&rft_id=info:doi/10.48550/arxiv.2202.10463&rft_dat=%3Carxiv_GOX%3E2202_10463%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 |