{"id":"https://openalex.org/W7214937646","doi":"https://doi.org/10.48550/arxiv.2609.35846","title":"Exponent Profiles of Oscillatory Matrices under Matrix and Inverse Sparsity","display_name":"Exponent Profiles of Oscillatory Matrices under Matrix and Inverse Sparsity","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214937646","doi":"https://doi.org/10.48550/arxiv.2609.35846"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35846","pdf_url":"https://arxiv.org/pdf/2609.35846","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":null,"license_id":null,"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/2609.35846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153617218","display_name":"Wei Xie","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xie, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153617218"],"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":0.9829000234603882,"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":0.9829000234603882,"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":0.011300000362098217,"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/T11476","display_name":"Graph theory and applications","score":0.002099999925121665,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matrix-sparsity","display_name":"matrix sparsity","score":0.7390000224113464},{"id":"https://openalex.org/keywords/symmetric-matrices","display_name":"symmetric matrices","score":0.7260000109672546}],"concepts":[{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7473999857902527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7013999819755554},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6367999911308289},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.5995000004768372},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5895000100135803},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5763999819755554},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.553600013256073},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5105000138282776},{"id":"https://openalex.org/C62555958","wikidata":"https://www.wikidata.org/wiki/Q6042601","display_name":"Integer matrix","level":5,"score":0.364300012588501},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3346000015735626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3181999921798706},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.3084000051021576},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28619998693466187},{"id":"https://openalex.org/C76134657","wikidata":"https://www.wikidata.org/wiki/Q370634","display_name":"Generalized inverse","level":3,"score":0.2700999975204468},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.25369998812675476}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35846","pdf_url":"https://arxiv.org/pdf/2609.35846","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.35846","doi":"https://doi.org/10.48550/arxiv.2609.35846","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35846","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.35846","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35846","pdf_url":"https://arxiv.org/pdf/2609.35846","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":null,"license_id":null,"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/W7214937646.pdf","grobid_xml":"https://content.openalex.org/works/W7214937646.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1966982704","https://openalex.org/W2026752664","https://openalex.org/W2054663063","https://openalex.org/W2058641279","https://openalex.org/W2072216899","https://openalex.org/W2982226092","https://openalex.org/W3044113988","https://openalex.org/W4385741141","https://openalex.org/W4395065461","https://openalex.org/W7212015720"],"related_works":["https://openalex.org/W7212015720","https://openalex.org/W2982226092","https://openalex.org/W2030984313","https://openalex.org/W1966982704","https://openalex.org/W1974276972","https://openalex.org/W2019839330","https://openalex.org/W3044113988","https://openalex.org/W2079488537","https://openalex.org/W1625339067","https://openalex.org/W2917474477"],"abstract_inverted_index":{"We":[0],"classify":[1],"the":[2,18,34,59,65,88,100],"simultaneous":[3],"half-bandwidths":[4],"$p,q$":[5],"of":[6,43,46,94],"a":[7,91,105,108],"symmetric":[8,89],"oscillatory":[9,102],"matrix":[10],"$A$":[11],"and":[12,24,50,116,120],"its":[13],"inverse.":[14],"At":[15],"order":[16,44],"$n\\ge2$,":[17],"possible":[19],"pairs":[20,26],"are":[21,48],"$(1,n-1)$,":[22],"$(n-1,1)$,":[23],"all":[25,41],"with":[27,58,72],"$2\\le":[28],"p,q\\le":[29],"n-1$.":[30],"Let":[31],"$e_k(A)$":[32],"be":[33],"least":[35],"positive":[36,109],"integer":[37,56,110],"$m$":[38],"for":[39,54,123],"which":[40],"minors":[42],"$k$":[45],"$A^m$":[47],"positive,":[49],"let":[51],"$e(A)=\\max_{1\\le":[52],"kr\\}$":[53],"every":[55,83],"$r\\ge\\lfloor(n-1)/2\\rfloor$,":[57],"starting":[60],"point":[61],"optimal.":[62],"With":[63],"$\u03b4=\\ell(U)-n+1$,":[64],"exponent":[66],"sum":[67,93],"satisfies":[68],"$\u03b4\\le":[69],"n(n-1)/2-\\sum_{k=1}^{n-1}e_k(A)":[70],"\\le\\lfloor(n-1)/2\\rfloor\u03b4$,":[71],"both":[73],"constants":[74],"sharp.":[75],"The":[76],"lower":[77],"deficit":[78],"bound":[79],"is":[80,113],"attained":[81],"at":[82],"admissible":[84],"factor":[85],"count.":[86],"Within":[87],"class,":[90,103],"total":[92],"$n(n-1)/2$":[95],"characterizes":[96],"basic":[97,101],"matrices.":[98],"In":[99],"without":[104],"symmetry":[106],"assumption,":[107],"vector":[111],"$(f_1,\\ldots,f_{n-1})$":[112],"realizable":[114],"if":[115,118],"only":[117],"$f_k\\le\\max\\{k,n-k\\}$":[119],"$f_k+f_{n-k}\\ge":[121],"n$":[122],"$1\\le":[124],"k":[125]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-01T00:00:00"}
