{"id":"https://openalex.org/W7204170188","doi":"https://doi.org/10.48550/arxiv.2608.22829","title":"Sign Propagation of Principal Minors in Fully Semimonotone Matrices and Stone's Conjecture","display_name":"Sign Propagation of Principal Minors in Fully Semimonotone Matrices and Stone's Conjecture","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204170188","doi":"https://doi.org/10.48550/arxiv.2608.22829"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.22829","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22829","pdf_url":"https://arxiv.org/pdf/2608.22829","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.22829","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005653520","display_name":"Sajal Ghosh","orcid":"https://orcid.org/0000-0002-6578-1691","observed_orcids":["https://orcid.org/0000-0002-6578-1691"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ghosh, Sajal","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5005653520"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9702000021934509,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0142000000923872,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.00139999995008111,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/principal-minors","display_name":"principal minors","score":0.9070000052452087}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8134999871253967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7649000287055969},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5616000294685364},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5597000122070312},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5422999858856201},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.5270000100135803},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5209000110626221},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5092999935150146},{"id":"https://openalex.org/C206743973","wikidata":"https://www.wikidata.org/wiki/Q178377","display_name":"Mathematical induction","level":2,"score":0.4778999984264374},{"id":"https://openalex.org/C2988995629","wikidata":"https://www.wikidata.org/wiki/Q2915729","display_name":"Matrix algebra","level":3,"score":0.3946000039577484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39430001378059387},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3772999942302704},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.34119999408721924},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.27320000529289246},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.2718999981880188},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.2533000111579895},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.22829","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22829","pdf_url":"https://arxiv.org/pdf/2608.22829","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.22829","doi":"https://doi.org/10.48550/arxiv.2608.22829","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.22829","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.22829","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.22829","pdf_url":"https://arxiv.org/pdf/2608.22829","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204170188.pdf","grobid_xml":"https://content.openalex.org/works/W7204170188.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1981752806","https://openalex.org/W2075691479","https://openalex.org/W4365384792","https://openalex.org/W182963890","https://openalex.org/W1992629784","https://openalex.org/W1998662097","https://openalex.org/W1580220309","https://openalex.org/W2913918357","https://openalex.org/W2374679732","https://openalex.org/W7099686192"],"abstract_inverted_index":{"Stone":[0],"conjectured":[1],"in":[2,66,136,160,184],"1981":[3],"that":[4,72,122,143,169,177,186,196],"every":[5,82],"fully":[6,34],"semimonotone":[7,35],"$\\mathbf{Q}_0$-matrix":[8],"is":[9,79,102,117,153,188],"a":[10,103,109,118,123,144],"$\\mathbf{P}_0$-matrix;":[11],"Murthy":[12],"and":[13,23,87,105,142,162,195],"Parthasarathy":[14],"(1995)":[15],"proved":[16],"this":[17],"for":[18,24],"orders":[19],"up":[20],"to":[21],"$4$":[22],"several":[25],"special":[26],"classes.":[27],"We":[28,70,120],"study":[29],"the":[30,44,49,73,76,90,137,170],"principal":[31,77,100,139,145],"minors":[32,116,131],"of":[33,75,85,92,147],"matrices":[36,199],"$A\\in\\Ezerof$":[37],"without":[38],"using":[39],"$\\Qzero$.":[40,204],"Let":[41],"$\\G(A)$":[42],"be":[43],"graph":[45],"whose":[46,157],"vertices":[47,60],"are":[48],"index":[50],"sets":[51],"$\u03b1$":[52],"with":[53,97,150,200],"$\\det":[54,178,201],"A_{\u03b1\u03b1}\\neq":[55],"0$":[56],"(including":[57],"$\u03b1=\\emptyset$),":[58],"two":[59,127],"being":[61],"adjacent":[62],"when":[63],"they":[64],"differ":[65],"exactly":[67],"one":[68],"index.":[69],"prove":[71],"sign":[74,124],"minor":[78,101],"constant":[80],"on":[81,89,113],"connected":[83],"component":[84,91,171],"$\\G(A)$,":[86],"positive":[88,134],"$\\emptyset$.":[93],"Consequences:":[94],"an":[95,154],"$\\Ezerof$-matrix":[96,107],"no":[98],"vanishing":[99,130],"$\\mathbf{P}$-matrix,":[104],"any":[106],"satisfying":[108],"simple":[110],"``descending''":[111],"condition":[112],"its":[114],"nonvanishing":[115],"$\\mathbf{P}_0$-matrix.":[119],"show":[121,168],"change":[125],"across":[126],"steps":[128],"through":[129],"forces":[132],"strictly":[133],"coupling":[135],"corresponding":[138],"pivotal":[140],"transform,":[141],"submatrix":[146],"minimal":[148],"order":[149],"negative":[151,175],"determinant":[152],"almost-$\\mathbf{P}_0$":[155],"matrix":[156],"inverse":[158],"lies":[159],"$\\Ezerof\\cap\\Nzero$":[161],"has":[163],"zero":[164],"diagonal.":[165],"Explicit":[166],"examples":[167],"structure":[172],"can":[173],"contain":[174],"components,":[176],"A>0$":[179,202],"does":[180],"not":[181,189],"force":[182],"$A\\in\\Pzero$":[183],"$\\Ezerof$,":[185],"$\\Ezerof$":[187],"invariant":[190],"under":[191],"$A\\mapsto":[192],"A+\\varepsilon":[193],"I$,":[194],"$\\Ezerof\\cap\\Pzero$":[197],"contains":[198],"outside":[203],"Stone's":[205],"conjecture":[206],"itself":[207],"remains":[208],"open.":[209]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-26T00:00:00"}