{"id":"https://openalex.org/W7223674513","doi":"https://doi.org/10.48550/arxiv.2610.31901","title":"Associated primes and v-numbers of integral closures of powers of edge ideals","display_name":"Associated primes and v-numbers of integral closures of powers of edge ideals","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223674513","doi":"https://doi.org/10.48550/arxiv.2610.31901"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.31901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31901","pdf_url":"https://arxiv.org/pdf/2610.31901","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/2610.31901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082827146","display_name":"Trung Chau","orcid":"https://orcid.org/0009-0002-6047-4841","observed_orcids":["https://orcid.org/0009-0002-6047-4841"]},"institutions":[{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]},{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]},{"id":"https://openalex.org/I70349855","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50","country_code":"VN","type":"government","lineage":["https://openalex.org/I70349855"]}],"countries":["CA","VN"],"is_corresponding":false,"raw_author_name":"Chau, Trung","raw_affiliation_strings":["Department of Mathematics , University of Manitoba , 420 Machray Hall , 186 Dysart Road , Win- nipeg , MB R3T 2N2 Canada","Institute of Mathematics , VAST , 18 Hoang Quoc Viet , Hanoi , Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Manitoba , 420 Machray Hall , 186 Dysart Road , Win- nipeg , MB R3T 2N2 Canada","institution_ids":["https://openalex.org/I46247651"]},{"raw_affiliation_string":"Institute of Mathematics , VAST , 18 Hoang Quoc Viet , Hanoi , Vietnam","institution_ids":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081973849","display_name":"Tai Huy Ha","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ha, Tai Huy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025169288","display_name":"Thanh Vu","orcid":"https://orcid.org/0000-0003-1967-397X","observed_orcids":["https://orcid.org/0000-0003-1967-397X"]},"institutions":[{"id":"https://openalex.org/I46247651","display_name":"University of Manitoba","ror":"https://ror.org/02gfys938","country_code":"CA","type":"education","lineage":["https://openalex.org/I46247651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Vu, Thanh","raw_affiliation_strings":["Department of Mathematics , University of Manitoba , 420 Machray Hall , 186 Dysart Road , Win- nipeg , MB R3T 2N2 Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Manitoba , 420 Machray Hall , 186 Dysart Road , Win- nipeg , MB R3T 2N2 Canada","institution_ids":["https://openalex.org/I46247651"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"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":0.9990000128746033,"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":0.9990000128746033,"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/T11703","display_name":"Rings, Modules, and Algebras","score":9.999999747378752e-05,"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":9.999999747378752e-05,"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/edge-ideals","display_name":"edge ideals","score":0.9700000286102295},{"id":"https://openalex.org/keywords/integral-closure","display_name":"integral closure","score":0.7739999890327454},{"id":"https://openalex.org/keywords/powers-of-ideals","display_name":"powers of ideals","score":0.8050000071525574},{"id":"https://openalex.org/keywords/associated-primes","display_name":"associated primes","score":0.9430000185966492},{"id":"https://openalex.org/keywords/v-number","display_name":"V-number","score":0.9430000185966492},{"id":"https://openalex.org/keywords/finite-simple-graphs","display_name":"finite simple graphs","score":0.847000002861023},{"id":"https://openalex.org/keywords/monomial-ideals","display_name":"monomial ideals","score":0.8610000014305115},{"id":"https://openalex.org/keywords/symbolic-power","display_name":"symbolic power","score":0.46799999475479126},{"id":"https://openalex.org/keywords/commutative-algebra-of-graphs","display_name":"commutative algebra of graphs","score":0.5889999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8317000269889832},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.48100000619888306},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46399998664855957},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.45019999146461487},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.444599986076355},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.44279998540878296},{"id":"https://openalex.org/C2777019822","wikidata":"https://www.wikidata.org/wiki/Q390066","display_name":"Containment (computer programming)","level":2,"score":0.43130001425743103},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4302999973297119},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.42399999499320984},{"id":"https://openalex.org/C182817911","wikidata":"https://www.wikidata.org/wiki/Q1497184","display_name":"Fractional ideal","level":3,"score":0.39320001006126404},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.3391999900341034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28949999809265137}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.31901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31901","pdf_url":"https://arxiv.org/pdf/2610.31901","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.2610.31901","doi":"https://doi.org/10.48550/arxiv.2610.31901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.31901","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.31901","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.31901","pdf_url":"https://arxiv.org/pdf/2610.31901","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/W7223674513.pdf","grobid_xml":"https://content.openalex.org/works/W7223674513.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W3190398951","https://openalex.org/W4409509035","https://openalex.org/W4417258196","https://openalex.org/W7204590695","https://openalex.org/W7211897881"],"related_works":["https://openalex.org/W2964312789","https://openalex.org/W3190398951","https://openalex.org/W7133506298","https://openalex.org/W7211897881","https://openalex.org/W2204453436","https://openalex.org/W2964085143","https://openalex.org/W4414761053","https://openalex.org/W4416117037","https://openalex.org/W2038699511","https://openalex.org/W7223114546"],"abstract_inverted_index":{"Let":[0],"$I":[1],"=":[2],"I(G)$":[3],"be":[4],"the":[5,16,19,33,38,83],"edge":[6],"ideal":[7],"of":[8,24,79],"a":[9],"finite":[10],"simple":[11],"graph":[12],"$G$.":[13],"We":[14],"investigate":[15],"relationship":[17],"between":[18],"associated":[20,39],"primes":[21],"and":[22,27,60,73,88],"$v$-numbers":[23],"powers":[25],"$I^t$":[26],"their":[28],"integral":[29],"closures":[30],"$\\overline{I^t}$.":[31],"For":[32],"third":[34],"power,":[35],"we":[36,56,76],"establish":[37],"prime":[40],"containment":[41],"$\\operatorname{Ass}(S/\\overline{I^3})":[42],"\\subseteq":[43],"\\operatorname{Ass}(S/I^3)$,":[44],"which":[45,82],"yields":[46],"$v(I^3)":[47],"\\le":[48],"v(\\overline{I^3})$.":[49],"In":[50],"contrast,":[51],"for":[52,67,81],"$t":[53,70],"\\ge":[54,71],"4$,":[55,75],"show":[57],"that":[58],"$\\operatorname{Ass}(S/\\overline{I^t})$":[59],"$\\operatorname{Ass}(S/I^t)$":[61],"are":[62,90],"in":[63],"general":[64],"incomparable.":[65],"Furthermore,":[66],"every":[68],"fixed":[69],"3$":[72],"$r\\ge":[74],"construct":[77],"families":[78],"graphs":[80],"discrepancies":[84],"$v(\\overline{I^t})":[85],"-":[86],"v(I^t)$":[87],"$v(I^r)-v(\\overline{I^r})$":[89],"arbitrarily":[91],"large.":[92]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-27T00:00:00"}