Maximal Generalized Rank in Graphical Matrix Spaces

In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-12
Main Authors: Guterman, Alexander, Meshulam, Roy, Spiridonov, Igor
Format: Article
Language:English
Subjects:
Combinatorial analysis
Graph theory
Subspaces
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by
cites
container_end_page
container_issue
container_start_page
container_title arXiv.org
container_volume
creator Guterman, Alexander
Meshulam, Roy
Spiridonov, Igor
description In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.
doi_str_mv 10.48550/arxiv.2212.11193
format article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2756878372</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2756878372</sourcerecordid><originalsourceid>FETCH-LOGICAL-a953-3d1ab830e66eb34fffad8be78945270ccaeb8609ce462ee4a32974042b9a0d7b3</originalsourceid><addsrcrecordid>eNotjU1Lw0AUABdBsNT-AG8Bz4m77-3nUYpWoUXQ3svb5AW3xjRuWgn-egt6msPAjBA3SlbaGyPvKE_puwJQUCmlAl6IGSCq0muAK7EYx72UEqwDY3AmcENT-qSuWHHPmbr0w03xSv1HkfpilWl4T_XZbuiY01S8DVTzeC0uW-pGXvxzLraPD9vlU7l-WT0v79clBYMlNoqiR8nWckTdti01PrLzQRtwsq6Jo7cy1KwtMGtCCE5LDTGQbFzEubj9yw758HXi8bjbH065Px934Iz1zqMD_AXeKkXb</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2756878372</pqid></control><display><type>article</type><title>Maximal Generalized Rank in Graphical Matrix Spaces</title><source>Publicly Available Content Database</source><creator>Guterman, Alexander ; Meshulam, Roy ; Spiridonov, Igor</creator><creatorcontrib>Guterman, Alexander ; Meshulam, Roy ; Spiridonov, Igor</creatorcontrib><description>In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.2212.11193</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Combinatorial analysis ; Graph theory ; Subspaces</subject><ispartof>arXiv.org, 2022-12</ispartof><rights>2022. 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>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2756878372?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>776,780,25731,27902,36989,44566</link.rule.ids></links><search><creatorcontrib>Guterman, Alexander</creatorcontrib><creatorcontrib>Meshulam, Roy</creatorcontrib><creatorcontrib>Spiridonov, Igor</creatorcontrib><title>Maximal Generalized Rank in Graphical Matrix Spaces</title><title>arXiv.org</title><description>In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.</description><subject>Combinatorial analysis</subject><subject>Graph theory</subject><subject>Subspaces</subject><issn>2331-8422</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNotjU1Lw0AUABdBsNT-AG8Bz4m77-3nUYpWoUXQ3svb5AW3xjRuWgn-egt6msPAjBA3SlbaGyPvKE_puwJQUCmlAl6IGSCq0muAK7EYx72UEqwDY3AmcENT-qSuWHHPmbr0w03xSv1HkfpilWl4T_XZbuiY01S8DVTzeC0uW-pGXvxzLraPD9vlU7l-WT0v79clBYMlNoqiR8nWckTdti01PrLzQRtwsq6Jo7cy1KwtMGtCCE5LDTGQbFzEubj9yw758HXi8bjbH065Px934Iz1zqMD_AXeKkXb</recordid><startdate>20221221</startdate><enddate>20221221</enddate><creator>Guterman, Alexander</creator><creator>Meshulam, Roy</creator><creator>Spiridonov, Igor</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>20221221</creationdate><title>Maximal Generalized Rank in Graphical Matrix Spaces</title><author>Guterman, Alexander ; Meshulam, Roy ; Spiridonov, Igor</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a953-3d1ab830e66eb34fffad8be78945270ccaeb8609ce462ee4a32974042b9a0d7b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Combinatorial analysis</topic><topic>Graph theory</topic><topic>Subspaces</topic><toplevel>online_resources</toplevel><creatorcontrib>Guterman, Alexander</creatorcontrib><creatorcontrib>Meshulam, Roy</creatorcontrib><creatorcontrib>Spiridonov, Igor</creatorcontrib><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</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><jtitle>arXiv.org</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Guterman, Alexander</au><au>Meshulam, Roy</au><au>Spiridonov, Igor</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Maximal Generalized Rank in Graphical Matrix Spaces</atitle><jtitle>arXiv.org</jtitle><date>2022-12-21</date><risdate>2022</risdate><eissn>2331-8422</eissn><abstract>In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.</abstract><cop>Ithaca</cop><pub>Cornell University Library, arXiv.org</pub><doi>10.48550/arxiv.2212.11193</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier EISSN: 2331-8422
ispartof arXiv.org, 2022-12
issn 2331-8422
language eng
recordid cdi_proquest_journals_2756878372
source Publicly Available Content Database
subjects Combinatorial analysis
Graph theory
Subspaces
title Maximal Generalized Rank in Graphical Matrix Spaces
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-06T23%3A27%3A55IST&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:journal&rft.genre=article&rft.atitle=Maximal%20Generalized%20Rank%20in%20Graphical%20Matrix%20Spaces&rft.jtitle=arXiv.org&rft.au=Guterman,%20Alexander&rft.date=2022-12-21&rft.eissn=2331-8422&rft_id=info:doi/10.48550/arxiv.2212.11193&rft_dat=%3Cproquest%3E2756878372%3C/proquest%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a953-3d1ab830e66eb34fffad8be78945270ccaeb8609ce462ee4a32974042b9a0d7b3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2756878372&rft_id=info:pmid/&rfr_iscdi=true