{"id":"https://openalex.org/W7118931713","doi":"https://doi.org/10.48550/arxiv.2601.01012","title":"Bad News for Couples: Tight Lower Bounds for Fair Division of Indivisible Items","display_name":"Bad News for Couples: Tight Lower Bounds for Fair Division of Indivisible Items","publication_year":2026,"publication_date":"2026-01-03","ids":{"openalex":"https://openalex.org/W7118931713","doi":"https://doi.org/10.48550/arxiv.2601.01012"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2601.01012","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.01012","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2601.01012","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007089239","display_name":"Max Dupre la Tour","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"la Tour, Max Dupr\u00e9","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007089239"],"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9836000204086304,"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":0.9836000204086304,"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/T11182","display_name":"Auction Theory and Applications","score":0.004399999976158142,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11031","display_name":"Game Theory and Applications","score":0.0038999998942017555,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6913999915122986},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.5936999917030334},{"id":"https://openalex.org/keywords/fair-division","display_name":"Fair division","score":0.4187000095844269},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.3822000026702881},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.2946000099182129}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6913999915122986},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.5936999917030334},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.48649999499320984},{"id":"https://openalex.org/C184659173","wikidata":"https://www.wikidata.org/wiki/Q1511081","display_name":"Fair division","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4169999957084656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38359999656677246},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33169999718666077},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.31130000948905945},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C31084985","wikidata":"https://www.wikidata.org/wiki/Q372650","display_name":"Common knowledge (logic)","level":5,"score":0.27079999446868896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2653999924659729}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2601.01012","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.01012","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2601.01012","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2601.01012","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.5221310257911682,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,22],"consider":[1],"the":[2,47,51],"problem":[3],"of":[4,15,28,54,87],"fairly":[5],"allocating":[6,29],"indivisible":[7,30],"goods":[8],"to":[9,32,39,60,80],"couples,":[10],"where":[11],"each":[12],"couple":[13],"consists":[14],"two":[16],"agents":[17,65],"with":[18,63],"distinct":[19],"additive":[20],"valuations.":[21],"show":[23],"that":[24,74],"there":[25],"exist":[26],"instances":[27,62,84],"items":[31,41],"$n$":[33,64],"couples":[34],"for":[35,83],"which":[36,58],"envy-freeness":[37],"up":[38],"$\u03a9(\\sqrt{n})$":[40],"cannot":[42],"be":[43,81],"guaranteed.":[44],"This":[45,68],"closes":[46],"gap":[48],"by":[49],"matching":[50],"upper":[52,75],"bound":[53,76],"Manurangsi":[55],"and":[56],"Suksompong,":[57],"applies":[59],"arbitrary":[61],"in":[66],"total.":[67],"result":[69],"is":[70],"somewhat":[71],"surprising,":[72],"as":[73],"was":[77],"conjectured":[78],"not":[79],"tight":[82],"consisting":[85],"only":[86],"small":[88],"groups.":[89]},"counts_by_year":[],"updated_date":"2026-01-08T20:10:11.968330","created_date":"2026-01-08T00:00:00"}