{"id":"https://openalex.org/W7214734251","doi":"https://doi.org/10.48550/arxiv.2609.32955","title":"The F-signature of Determinantal Rings","display_name":"The F-signature of Determinantal Rings","publication_year":2026,"publication_date":"2026-09-26","ids":{"openalex":"https://openalex.org/W7214734251","doi":"https://doi.org/10.48550/arxiv.2609.32955"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.32955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32955","pdf_url":"https://arxiv.org/pdf/2609.32955","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/2609.32955","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153426372","display_name":"Hang Huang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Hang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5153515667","display_name":"Cheng Mend","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meng, Cheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044863958","display_name":"Swaraj Pande","orcid":"https://orcid.org/0000-0003-2324-9434","observed_orcids":["https://orcid.org/0000-0003-2324-9434"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pande, Suchitra","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011181313","display_name":"Yevgeniya Tarasova","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tarasova, Yevgeniya","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":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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.001500000013038516,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/f-signature","display_name":"F-signature","score":0.9990000128746033},{"id":"https://openalex.org/keywords/positive-characteristic","display_name":"positive characteristic","score":0.6499999761581421},{"id":"https://openalex.org/keywords/toric-degenerations","display_name":"toric degenerations","score":0.8920000195503235},{"id":"https://openalex.org/keywords/grobner-bases","display_name":"Gr\u00f6bner bases","score":0.7850000262260437},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"upper and lower bounds","score":0.6480000019073486}],"concepts":[{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.7993000149726868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7742000222206116},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5796999931335449},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5097000002861023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4846999943256378},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4779999852180481},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4429999887943268},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.43939998745918274},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3156999945640564},{"id":"https://openalex.org/C72010251","wikidata":"https://www.wikidata.org/wiki/Q5265688","display_name":"Determinantal point process","level":4,"score":0.310699999332428},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27900001406669617},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.32955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32955","pdf_url":"https://arxiv.org/pdf/2609.32955","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.2609.32955","doi":"https://doi.org/10.48550/arxiv.2609.32955","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.32955","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:2609.32955","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.32955","pdf_url":"https://arxiv.org/pdf/2609.32955","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214734251.pdf","grobid_xml":"https://content.openalex.org/works/W7214734251.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1701609513"],"related_works":["https://openalex.org/W4396651038","https://openalex.org/W4405391534","https://openalex.org/W7216287351","https://openalex.org/W2951946157","https://openalex.org/W7097229310","https://openalex.org/W1965067799","https://openalex.org/W4312032766","https://openalex.org/W2897502188","https://openalex.org/W2511299486","https://openalex.org/W7167597097"],"abstract_inverted_index":{"Let":[0],"$R_{n,p}$":[1],"be":[2,88],"the":[3,9,33,38,51,64,76],"determinantal":[4],"hypersurface":[5],"ring":[6],"defined":[7],"by":[8],"determinant":[10],"of":[11,35,53,73,78],"a":[12,69,82],"generic":[13],"$n":[14,22],"\\times":[15],"n$":[16],"matrix":[17],"in":[18,48],"characteristic":[19],"$p$":[20],"where":[21],"\\geq":[23],"2$.":[24],"In":[25],"this":[26,44],"paper,":[27],"we":[28,41,67],"obtain":[29],"explicit":[30],"bounds":[31],"for":[32],"$F$-signature":[34,45,52,77,86],"$R_{n,p}$.":[36],"For":[37,63],"upper":[39,58],"bound,":[40,59,66],"prove":[42],"that":[43],"is":[46,61,100],"decreasing":[47],"$n$,":[49],"so":[50,75],"$R_{2,p}$":[54],"serves":[55,80],"as":[56,81],"an":[57],"which":[60],"$2/3$.":[62],"lower":[65,83],"find":[68],"toric":[70],"degeneration":[71],"$B_n$":[72,79],"$R_{n,p}$,":[74],"bound.":[84],"This":[85],"can":[87],"computed":[89],"using":[90],"either":[91],"Gr\u00f6bner":[92],"basis":[93],"or":[94],"Han-Monsky":[95],"machinery,":[96],"and":[97],"its":[98],"value":[99],"$\\frac{(n!)^2}{(2n-1)!}$.":[101]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}
