Arithmetical Structures on Coconut Trees
If G is a finite connected graph, then an arithmetical structure on \(G\) is a pair of vectors \((\mathbf{d}, \mathbf{r})\) with positive integer entries such that \((\diag(\mathbf{d}) - A)\cdot \mathbf{r} = \mathbf{0}\), where \(A\) is the adjacency matrix of \(G\) and the entries of \(\mathbf{r}\)...
Gespeichert in:
| Veröffentlicht in: | arXiv.org 2024-06 |
|---|---|
| Hauptverfasser: | , , , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | arXiv.org |
| container_volume | |
| creator | Diaz-Lopez, Alexander Ha, Brian Harris, Pamela E Rogers, Jonathan Koss, Theo Smith, Dorian |
| description | If G is a finite connected graph, then an arithmetical structure on \(G\) is a pair of vectors \((\mathbf{d}, \mathbf{r})\) with positive integer entries such that \((\diag(\mathbf{d}) - A)\cdot \mathbf{r} = \mathbf{0}\), where \(A\) is the adjacency matrix of \(G\) and the entries of \(\mathbf{r}\) have no common factor other than \(1\). In this paper, we generalize the result of Archer, Bishop, Diaz-Lopez, García Puente, Glass, and Louwsma on enumerating arithmetical structures on bidents (also called coconut tree graphs \(\CT{p}{2}\)) to all coconut tree graphs \(\CT{p}{s}\) which consists of a path on \(p>0\) vertices to which we append \(s>0\) leaves to the right most vertex on the path. We also give a characterization of smooth arithmetical structures on coconut trees when given number assignments to the leaf nodes. |
| format | Article |
| fullrecord | <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_3069349276</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3069349276</sourcerecordid><originalsourceid>FETCH-proquest_journals_30693492763</originalsourceid><addsrcrecordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQcCzKLMnITS3JTE7MUQguKSpNLiktSi1WyM9TcM5Pzs8rLVEIKUpNLeZhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWfmlRXlAqXhjAzNLYxNLI3MzY-JUAQDE1DBl</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3069349276</pqid></control><display><type>article</type><title>Arithmetical Structures on Coconut Trees</title><source>Free E- Journals</source><creator>Diaz-Lopez, Alexander ; Ha, Brian ; Harris, Pamela E ; Rogers, Jonathan ; Koss, Theo ; Smith, Dorian</creator><creatorcontrib>Diaz-Lopez, Alexander ; Ha, Brian ; Harris, Pamela E ; Rogers, Jonathan ; Koss, Theo ; Smith, Dorian</creatorcontrib><description>If G is a finite connected graph, then an arithmetical structure on \(G\) is a pair of vectors \((\mathbf{d}, \mathbf{r})\) with positive integer entries such that \((\diag(\mathbf{d}) - A)\cdot \mathbf{r} = \mathbf{0}\), where \(A\) is the adjacency matrix of \(G\) and the entries of \(\mathbf{r}\) have no common factor other than \(1\). In this paper, we generalize the result of Archer, Bishop, Diaz-Lopez, García Puente, Glass, and Louwsma on enumerating arithmetical structures on bidents (also called coconut tree graphs \(\CT{p}{2}\)) to all coconut tree graphs \(\CT{p}{s}\) which consists of a path on \(p>0\) vertices to which we append \(s>0\) leaves to the right most vertex on the path. We also give a characterization of smooth arithmetical structures on coconut trees when given number assignments to the leaf nodes.</description><identifier>EISSN: 2331-8422</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Apexes ; Graphs ; Trees (mathematics)</subject><ispartof>arXiv.org, 2024-06</ispartof><rights>2024. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</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>780,784</link.rule.ids></links><search><creatorcontrib>Diaz-Lopez, Alexander</creatorcontrib><creatorcontrib>Ha, Brian</creatorcontrib><creatorcontrib>Harris, Pamela E</creatorcontrib><creatorcontrib>Rogers, Jonathan</creatorcontrib><creatorcontrib>Koss, Theo</creatorcontrib><creatorcontrib>Smith, Dorian</creatorcontrib><title>Arithmetical Structures on Coconut Trees</title><title>arXiv.org</title><description>If G is a finite connected graph, then an arithmetical structure on \(G\) is a pair of vectors \((\mathbf{d}, \mathbf{r})\) with positive integer entries such that \((\diag(\mathbf{d}) - A)\cdot \mathbf{r} = \mathbf{0}\), where \(A\) is the adjacency matrix of \(G\) and the entries of \(\mathbf{r}\) have no common factor other than \(1\). In this paper, we generalize the result of Archer, Bishop, Diaz-Lopez, García Puente, Glass, and Louwsma on enumerating arithmetical structures on bidents (also called coconut tree graphs \(\CT{p}{2}\)) to all coconut tree graphs \(\CT{p}{s}\) which consists of a path on \(p>0\) vertices to which we append \(s>0\) leaves to the right most vertex on the path. We also give a characterization of smooth arithmetical structures on coconut trees when given number assignments to the leaf nodes.</description><subject>Apexes</subject><subject>Graphs</subject><subject>Trees (mathematics)</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNpjYuA0MjY21LUwMTLiYOAtLs4yMDAwMjM3MjU15mTQcCzKLMnITS3JTE7MUQguKSpNLiktSi1WyM9TcM5Pzs8rLVEIKUpNLeZhYE1LzClO5YXS3AzKbq4hzh66BUX5haWpxSXxWfmlRXlAqXhjAzNLYxNLI3MzY-JUAQDE1DBl</recordid><startdate>20240617</startdate><enddate>20240617</enddate><creator>Diaz-Lopez, Alexander</creator><creator>Ha, Brian</creator><creator>Harris, Pamela E</creator><creator>Rogers, Jonathan</creator><creator>Koss, Theo</creator><creator>Smith, Dorian</creator><general>Cornell University Library, arXiv.org</general><scope>8FE</scope><scope>8FG</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>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20240617</creationdate><title>Arithmetical Structures on Coconut Trees</title><author>Diaz-Lopez, Alexander ; Ha, Brian ; Harris, Pamela E ; Rogers, Jonathan ; Koss, Theo ; Smith, Dorian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_30693492763</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Apexes</topic><topic>Graphs</topic><topic>Trees (mathematics)</topic><toplevel>online_resources</toplevel><creatorcontrib>Diaz-Lopez, Alexander</creatorcontrib><creatorcontrib>Ha, Brian</creatorcontrib><creatorcontrib>Harris, Pamela E</creatorcontrib><creatorcontrib>Rogers, Jonathan</creatorcontrib><creatorcontrib>Koss, Theo</creatorcontrib><creatorcontrib>Smith, Dorian</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & 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>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content 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></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Diaz-Lopez, Alexander</au><au>Ha, Brian</au><au>Harris, Pamela E</au><au>Rogers, Jonathan</au><au>Koss, Theo</au><au>Smith, Dorian</au><format>book</format><genre>document</genre><ristype>GEN</ristype><atitle>Arithmetical Structures on Coconut Trees</atitle><jtitle>arXiv.org</jtitle><date>2024-06-17</date><risdate>2024</risdate><eissn>2331-8422</eissn><abstract>If G is a finite connected graph, then an arithmetical structure on \(G\) is a pair of vectors \((\mathbf{d}, \mathbf{r})\) with positive integer entries such that \((\diag(\mathbf{d}) - A)\cdot \mathbf{r} = \mathbf{0}\), where \(A\) is the adjacency matrix of \(G\) and the entries of \(\mathbf{r}\) have no common factor other than \(1\). In this paper, we generalize the result of Archer, Bishop, Diaz-Lopez, García Puente, Glass, and Louwsma on enumerating arithmetical structures on bidents (also called coconut tree graphs \(\CT{p}{2}\)) to all coconut tree graphs \(\CT{p}{s}\) which consists of a path on \(p>0\) vertices to which we append \(s>0\) leaves to the right most vertex on the path. We also give a characterization of smooth arithmetical structures on coconut trees when given number assignments to the leaf nodes.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | EISSN: 2331-8422 |
| ispartof | arXiv.org, 2024-06 |
| issn | 2331-8422 |
| language | eng |
| recordid | cdi_proquest_journals_3069349276 |
| source | Free E- Journals |
| subjects | Apexes Graphs Trees (mathematics) |
| title | Arithmetical Structures on Coconut Trees |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-05T02%3A42%3A48IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=document&rft.atitle=Arithmetical%20Structures%20on%20Coconut%20Trees&rft.jtitle=arXiv.org&rft.au=Diaz-Lopez,%20Alexander&rft.date=2024-06-17&rft.eissn=2331-8422&rft_id=info:doi/&rft_dat=%3Cproquest%3E3069349276%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3069349276&rft_id=info:pmid/&rfr_iscdi=true |