{"id":"https://openalex.org/W7220691365","doi":"https://doi.org/10.48550/arxiv.2610.04369","title":"Core Coordinates and Negative Support in A-Hypergeometric Systems","display_name":"Core Coordinates and Negative Support in A-Hypergeometric Systems","publication_year":2026,"publication_date":"2026-10-03","ids":{"openalex":"https://openalex.org/W7220691365","doi":"https://doi.org/10.48550/arxiv.2610.04369"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.04369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04369","pdf_url":"https://arxiv.org/pdf/2610.04369","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/2610.04369","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5095777220","display_name":"Mao Nagamine","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nagamine, Mao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5095777220"],"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":0.8432999849319458,"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":0.8432999849319458,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.051500000059604645,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.04349999874830246,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/a-hypergeometric-systems","display_name":"A-hypergeometric systems","score":0.996999979019165},{"id":"https://openalex.org/keywords/reduced-grobner-basis","display_name":"reduced Gr\u00f6bner basis","score":0.8040000200271606},{"id":"https://openalex.org/keywords/regular-triangulations","display_name":"regular triangulations","score":0.9520000219345093},{"id":"https://openalex.org/keywords/homogeneous-systems","display_name":"homogeneous systems","score":0.5979999899864197}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7396000027656555},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.695900022983551},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6956999897956848},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6478000283241272},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5841000080108643},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5134999752044678},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.48730000853538513},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4253000020980835},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4059000015258789},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38609999418258667},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3237999975681305},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.28600001335144043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2856000065803528},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C150591576","wikidata":"https://www.wikidata.org/wiki/Q739925","display_name":"Family of sets","level":3,"score":0.2770000100135803},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C2780366209","wikidata":"https://www.wikidata.org/wiki/Q5170200","display_name":"Core model","level":2,"score":0.25}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.04369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04369","pdf_url":"https://arxiv.org/pdf/2610.04369","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.2610.04369","doi":"https://doi.org/10.48550/arxiv.2610.04369","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.04369","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:2610.04369","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.04369","pdf_url":"https://arxiv.org/pdf/2610.04369","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/W7220691365.pdf","grobid_xml":"https://content.openalex.org/works/W7220691365.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4394946674","https://openalex.org/W4410282714","https://openalex.org/W7172439043"],"related_works":["https://openalex.org/W4394946674","https://openalex.org/W1811158423","https://openalex.org/W4410282714","https://openalex.org/W2953147082","https://openalex.org/W2059013681","https://openalex.org/W2295798532","https://openalex.org/W1604819548","https://openalex.org/W1514035600","https://openalex.org/W7101088000","https://openalex.org/W2565187613"],"abstract_inverted_index":{"For":[0],"a":[1,16],"homogeneous":[2],"$A$-hypergeometric":[3],"system,":[4],"let":[5,21],"$K_v$":[6],"be":[7,23],"the":[8,11,24,60,69,74,79,92],"intersection":[9],"of":[10,26,28,39,62,87],"negative":[12],"support":[13],"family":[14,86],"for":[15,47,90],"fake":[17,52,88],"exponent":[18,53],"$v$,":[19],"and":[20,50,55,73],"$C_w$":[22],"set":[25],"indices":[27],"variables":[29],"that":[30,43],"do":[31],"not":[32],"occur":[33],"in":[34],"any":[35],"minimal":[36],"monomial":[37],"generator":[38],"$\\operatorname{in}_w(I_A)$.":[40],"We":[41,64],"prove":[42],"$K_v=\\operatorname{nsupp}(v)\\cap":[44],"C_w$":[45],"holds":[46],"every":[48,51],"parameter":[49],"if":[54,57],"only":[56],"$\\operatorname{Cone}(A_{C_w})$":[58],"meets":[59],"interior":[61],"$\\operatorname{Cone}(A)$.":[63],"give":[65],"equivalent":[66],"criteria":[67],"using":[68],"reduced":[70],"Gr\u00f6bner":[71],"basis":[72],"associated":[75],"regular":[76],"triangulation.":[77],"When":[78],"condition":[80],"fails,":[81],"we":[82],"construct":[83],"an":[84],"infinite":[85],"exponents":[89],"which":[91],"equality":[93],"fails.":[94]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-07T00:00:00"}
