{"id":"https://openalex.org/W7202416346","doi":null,"title":"Non-Existence of EFX Chore Allocations for Monotone Cost Functions with Binary Marginals","display_name":"Non-Existence of EFX Chore Allocations for Monotone Cost Functions with Binary Marginals","publication_year":2026,"publication_date":"2026-08-11","ids":{"openalex":"https://openalex.org/W7202416346"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.10572","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.10572","pdf_url":"https://arxiv.org/pdf/2608.10572","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.10572","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5130052596","display_name":"Zehan Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN","MO"],"is_corresponding":false,"raw_author_name":"Lin, Zehan","raw_affiliation_strings":["University of Macau Harbin Institute of Technology , Shenzhen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Macau Harbin Institute of Technology , Shenzhen","institution_ids":["https://openalex.org/I204512498","https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5147108113","display_name":"Shengxin Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]},{"id":"https://openalex.org/I204983213","display_name":"Harbin Institute of Technology","ror":"https://ror.org/01yqg2h08","country_code":"CN","type":"education","lineage":["https://openalex.org/I204983213"]}],"countries":["CN","MO"],"is_corresponding":false,"raw_author_name":"Liu, Shengxin","raw_affiliation_strings":["University of Macau Harbin Institute of Technology , Shenzhen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Macau Harbin Institute of Technology , Shenzhen","institution_ids":["https://openalex.org/I204512498","https://openalex.org/I204983213"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035538983","display_name":"Biaoshuai Tao","orcid":"https://orcid.org/0000-0003-4098-844X","observed_orcids":["https://orcid.org/0000-0003-4098-844X"]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Tao, Biaoshuai","raw_affiliation_strings":["Shanghai Jiao Tong University Nanyang Technological University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University Nanyang Technological University","institution_ids":["https://openalex.org/I172675005","https://openalex.org/I183067930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147098176","display_name":"Shengwei Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Zhou, Shengwei","raw_affiliation_strings":["Shanghai Jiao Tong University Nanyang Technological University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University Nanyang Technological University","institution_ids":["https://openalex.org/I172675005","https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10991","display_name":"Game Theory and Voting Systems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12288","display_name":"Optimization and Search Problems","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/indivisible-chores","display_name":"indivisible chores","score":0.9909999966621399},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.5799999833106995},{"id":"https://openalex.org/keywords/fair-division","display_name":"fair division","score":0.8109999895095825},{"id":"https://openalex.org/keywords/lean-4-formal-verification","display_name":"Lean 4 formal verification","score":0.8460000157356262}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7577999830245972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7450000047683716},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.7376000285148621},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.7182000279426575},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5540000200271606},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44859999418258667},{"id":"https://openalex.org/C185529760","wikidata":"https://www.wikidata.org/wiki/Q164307","display_name":"Binary operation","level":2,"score":0.33959999680519104},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C2778207910","wikidata":"https://www.wikidata.org/wiki/Q397610","display_name":"Agr\u00e9gation","level":3,"score":0.3147999942302704},{"id":"https://openalex.org/C178621042","wikidata":"https://www.wikidata.org/wiki/Q7631710","display_name":"Submodular set function","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2653000056743622}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:2608.10572","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.10572","pdf_url":"https://arxiv.org/pdf/2608.10572","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.10572","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.10572","pdf_url":"https://arxiv.org/pdf/2608.10572","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/W7202416346.pdf","grobid_xml":"https://content.openalex.org/works/W7202416346.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W7155047936","https://openalex.org/W7160600048","https://openalex.org/W7161952363","https://openalex.org/W7164000247"],"related_works":["https://openalex.org/W4386148574","https://openalex.org/W7161952363","https://openalex.org/W4375958183","https://openalex.org/W4401023945","https://openalex.org/W7164000247","https://openalex.org/W4285600192","https://openalex.org/W7213312984","https://openalex.org/W4404306973","https://openalex.org/W4416411507","https://openalex.org/W4389478426"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,27,48,62,77],"existence":[3,29,49],"of":[4,12,50],"envy-free":[5],"up":[6],"to":[7,33],"any":[8],"item":[9],"(EFX)":[10],"allocations":[11],"indivisible":[13,25],"chores":[14],"when":[15],"agents":[16],"have":[17,34],"monotone":[18,40],"cost":[19,85],"functions":[20,41],"with":[21,42,83],"binary":[22,43,88,94],"marginals.":[23,44],"For":[24,45],"goods,":[26],"corresponding":[28],"question":[30],"is":[31],"known":[32,55],"an":[35],"affirmative":[36],"answer":[37],"for":[38,57,87,93],"general":[39,63],"chores,":[46],"however,":[47],"EFX":[51,102],"allocation":[52,103],"was":[53],"previously":[54],"only":[56],"more":[58],"restricted":[59],"classes,":[60],"while":[61],"binary-marginal":[64],"case":[65],"remained":[66],"unresolved.":[67],"In":[68,97],"this":[69],"paper,":[70],"we":[71,108],"provide":[72],"two":[73],"counterexamples":[74],"based":[75],"on":[76],"same":[78],"18-agent,":[79],"53-chore":[80],"word":[81],"gadget,":[82],"one":[84],"profile":[86],"XOS":[89],"costs":[90],"and":[91,110],"another":[92],"supermodular":[95],"costs.":[96],"both":[98],"cases,":[99],"a":[100],"complete":[101],"need":[104],"not":[105],"exist.":[106],"Finally,":[107],"formalize":[109],"verify":[111],"our":[112],"main":[113],"results":[114],"in":[115],"Lean":[116],"4.":[117]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-14T00:00:00"}