Strongly nice property and Schur positivity of graphs
Motivated by the notion of nice graphs, we introduce the concept of strongly nice property, which can be used to study the Schur positivity of symmetric functions. We show that a graph and all its induced subgraphs are strongly nice if and only if it is claw-free, which strengthens a result of Stanl...
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 | Li, Ethan Y. H Li, Grace M. X Yang, Arthur L. B Zhang, Zhong-Xue |
| description | Motivated by the notion of nice graphs, we introduce the concept of strongly
nice property, which can be used to study the Schur positivity of symmetric
functions. We show that a graph and all its induced subgraphs are strongly nice
if and only if it is claw-free, which strengthens a result of Stanley and
provides further evidence for the well-known conjecture on the Schur positivity
of claw-free graphs. As another application, we solve Wang and Wang's
conjecture on the non-Schur positivity of squid graphs $Sq(2n-1;1^n)$ for $n
\ge 3$ by proving that these graphs are not strongly nice. |
| doi_str_mv | 10.48550/arxiv.2408.15074 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2408_15074</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2408_15074</sourcerecordid><originalsourceid>FETCH-arxiv_primary_2408_150743</originalsourceid><addsrcrecordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjGw0DM0NTA34WQwDS4pys9Lz6lUyMtMTlUoKMovSC0qqVRIzEtRCE7OKC1SKMgvzizJLMsECuanKaQXJRZkFPMwsKYl5hSn8kJpbgZ5N9cQZw9dsAXxBUWZuYlFlfEgi-LBFhkTVgEAnlMzIg</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Strongly nice property and Schur positivity of graphs</title><source>arXiv.org</source><creator>Li, Ethan Y. H ; Li, Grace M. X ; Yang, Arthur L. B ; Zhang, Zhong-Xue</creator><creatorcontrib>Li, Ethan Y. H ; Li, Grace M. X ; Yang, Arthur L. B ; Zhang, Zhong-Xue</creatorcontrib><description>Motivated by the notion of nice graphs, we introduce the concept of strongly
nice property, which can be used to study the Schur positivity of symmetric
functions. We show that a graph and all its induced subgraphs are strongly nice
if and only if it is claw-free, which strengthens a result of Stanley and
provides further evidence for the well-known conjecture on the Schur positivity
of claw-free graphs. As another application, we solve Wang and Wang's
conjecture on the non-Schur positivity of squid graphs $Sq(2n-1;1^n)$ for $n
\ge 3$ by proving that these graphs are not strongly nice.</description><identifier>DOI: 10.48550/arxiv.2408.15074</identifier><language>eng</language><subject>Mathematics - Combinatorics</subject><creationdate>2024-08</creationdate><rights>http://creativecommons.org/licenses/by-nc-nd/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2408.15074$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2408.15074$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Li, Ethan Y. H</creatorcontrib><creatorcontrib>Li, Grace M. X</creatorcontrib><creatorcontrib>Yang, Arthur L. B</creatorcontrib><creatorcontrib>Zhang, Zhong-Xue</creatorcontrib><title>Strongly nice property and Schur positivity of graphs</title><description>Motivated by the notion of nice graphs, we introduce the concept of strongly
nice property, which can be used to study the Schur positivity of symmetric
functions. We show that a graph and all its induced subgraphs are strongly nice
if and only if it is claw-free, which strengthens a result of Stanley and
provides further evidence for the well-known conjecture on the Schur positivity
of claw-free graphs. As another application, we solve Wang and Wang's
conjecture on the non-Schur positivity of squid graphs $Sq(2n-1;1^n)$ for $n
\ge 3$ by proving that these graphs are not strongly nice.</description><subject>Mathematics - Combinatorics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNpjYJA0NNAzsTA1NdBPLKrILNMzMjGw0DM0NTA34WQwDS4pys9Lz6lUyMtMTlUoKMovSC0qqVRIzEtRCE7OKC1SKMgvzizJLMsECuanKaQXJRZkFPMwsKYl5hSn8kJpbgZ5N9cQZw9dsAXxBUWZuYlFlfEgi-LBFhkTVgEAnlMzIg</recordid><startdate>20240827</startdate><enddate>20240827</enddate><creator>Li, Ethan Y. H</creator><creator>Li, Grace M. X</creator><creator>Yang, Arthur L. B</creator><creator>Zhang, Zhong-Xue</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20240827</creationdate><title>Strongly nice property and Schur positivity of graphs</title><author>Li, Ethan Y. H ; Li, Grace M. X ; Yang, Arthur L. B ; Zhang, Zhong-Xue</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_2408_150743</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Mathematics - Combinatorics</topic><toplevel>online_resources</toplevel><creatorcontrib>Li, Ethan Y. H</creatorcontrib><creatorcontrib>Li, Grace M. X</creatorcontrib><creatorcontrib>Yang, Arthur L. B</creatorcontrib><creatorcontrib>Zhang, Zhong-Xue</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Li, Ethan Y. H</au><au>Li, Grace M. X</au><au>Yang, Arthur L. B</au><au>Zhang, Zhong-Xue</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Strongly nice property and Schur positivity of graphs</atitle><date>2024-08-27</date><risdate>2024</risdate><abstract>Motivated by the notion of nice graphs, we introduce the concept of strongly
nice property, which can be used to study the Schur positivity of symmetric
functions. We show that a graph and all its induced subgraphs are strongly nice
if and only if it is claw-free, which strengthens a result of Stanley and
provides further evidence for the well-known conjecture on the Schur positivity
of claw-free graphs. As another application, we solve Wang and Wang's
conjecture on the non-Schur positivity of squid graphs $Sq(2n-1;1^n)$ for $n
\ge 3$ by proving that these graphs are not strongly nice.</abstract><doi>10.48550/arxiv.2408.15074</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.2408.15074 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_2408_15074 |
| source | arXiv.org |
| subjects | Mathematics - Combinatorics |
| title | Strongly nice property and Schur positivity of graphs |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-21T05%3A45%3A38IST&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=Strongly%20nice%20property%20and%20Schur%20positivity%20of%20graphs&rft.au=Li,%20Ethan%20Y.%20H&rft.date=2024-08-27&rft_id=info:doi/10.48550/arxiv.2408.15074&rft_dat=%3Carxiv_GOX%3E2408_15074%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 |