{"id":"https://openalex.org/W4417064297","doi":"https://doi.org/10.48550/arxiv.2509.08121","title":"An Algorithmic Upper Bound for Permanents via a Permanental Schur Inequality","display_name":"An Algorithmic Upper Bound for Permanents via a Permanental Schur Inequality","publication_year":2025,"publication_date":"2025-09-09","ids":{"openalex":"https://openalex.org/W4417064297","doi":"https://doi.org/10.48550/arxiv.2509.08121"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2509.08121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.08121","pdf_url":"https://arxiv.org/pdf/2509.08121","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,"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"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2509.08121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056555726","display_name":"Aditi Laddha","orcid":"https://orcid.org/0000-0002-9781-1402"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Laddha, Aditi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062209465","display_name":"Madhusudhan Reddy Pittu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pittu, Madhusudhan Reddy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.20250000059604645,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.20250000059604645,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.1875,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.16779999434947968,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/bounding-overwatch","display_name":"Bounding overwatch","score":0.810699999332428},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.7182999849319458},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6263999938964844},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.6067000031471252},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44940000772476196},{"id":"https://openalex.org/keywords/block-matrix","display_name":"Block matrix","score":0.39419999718666077}],"concepts":[{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.810699999332428},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7182999849319458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6682000160217285},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6263999938964844},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.6067000031471252},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4684000015258789},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44940000772476196},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4163999855518341},{"id":"https://openalex.org/C85817219","wikidata":"https://www.wikidata.org/wiki/Q884772","display_name":"Block matrix","level":3,"score":0.39419999718666077},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3785000145435333},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3407000005245209},{"id":"https://openalex.org/C84507854","wikidata":"https://www.wikidata.org/wiki/Q952222","display_name":"Diagonally dominant matrix","level":3,"score":0.33629998564720154},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30970001220703125},{"id":"https://openalex.org/C126312332","wikidata":"https://www.wikidata.org/wiki/Q2658","display_name":"Gaussian elimination","level":3,"score":0.30379998683929443},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2782999873161316},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.25760000944137573},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2509.08121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.08121","pdf_url":"https://arxiv.org/pdf/2509.08121","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,"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.2509.08121","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2509.08121","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,"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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2509.08121","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2509.08121","pdf_url":"https://arxiv.org/pdf/2509.08121","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,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Computing":[0],"the":[1,42,58],"permanent":[2],"of":[3,22],"a":[4,8,18,27],"non-negative":[5],"matrix":[6],"is":[7],"computationally":[9],"challenging,":[10],"\\#P-complete":[11],"problem":[12],"with":[13],"wide-ranging":[14],"applications.":[15],"We":[16],"introduce":[17,36],"novel":[19],"permanental":[20],"analogue":[21],"Schur's":[23],"determinant":[24],"formula,":[25],"leveraging":[26],"newly":[28],"defined":[29],"\\emph{permanental":[30],"inverse}.":[31],"Building":[32],"on":[33,57],"this,":[34],"we":[35],"an":[37],"iterative,":[38],"deterministic":[39],"procedure":[40],"called":[41],"\\emph{permanent":[43],"process},":[44],"analogous":[45],"to":[46],"Gaussian":[47],"elimination,":[48],"which":[49],"yields":[50],"constructive":[51],"and":[52,77,82],"algorithmically":[53],"computable":[54],"upper":[55],"bounds":[56],"permanent.":[59],"Our":[60],"framework":[61],"provides":[62],"particularly":[63],"strong":[64],"guarantees":[65],"for":[66,80],"matrices":[67],"exhibiting":[68],"approximate":[69],"diagonal":[70],"dominance-like":[71],"properties,":[72],"thereby":[73],"offering":[74],"new":[75],"theoretical":[76],"computational":[78],"tools":[79],"analyzing":[81],"bounding":[83],"permanents.":[84]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}