{"id":"https://openalex.org/W7219867474","doi":"https://doi.org/10.48550/arxiv.2610.05617","title":"Prime factorisation of stable-matching instances: uniqueness, simultaneous products, and an exact census","display_name":"Prime factorisation of stable-matching instances: uniqueness, simultaneous products, and an exact census","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7219867474","doi":"https://doi.org/10.48550/arxiv.2610.05617"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05617","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05617","pdf_url":"https://arxiv.org/pdf/2610.05617","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/2610.05617","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101482889","display_name":"Yoshiteru Ishida","orcid":"https://orcid.org/0000-0003-1641-5385","observed_orcids":["https://orcid.org/0000-0003-1641-5385"]},"institutions":[{"id":"https://openalex.org/I136259955","display_name":"Toyohashi University of Technology","ror":"https://ror.org/04ezg6d83","country_code":"JP","type":"education","lineage":["https://openalex.org/I136259955"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ishida, Yoshiteru","raw_affiliation_strings":["Toyohashi University of Technology , Toyohashi , Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toyohashi University of Technology , Toyohashi , Japan","institution_ids":["https://openalex.org/I136259955"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5101482889"],"corresponding_institution_ids":["https://openalex.org/I136259955"],"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/T10991","display_name":"Game Theory and Voting Systems","score":0.9897000193595886,"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":0.9897000193595886,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.006399999838322401,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.0015999999595806003,"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/stable-marriage-problem","display_name":"stable marriage problem","score":0.9929999709129333},{"id":"https://openalex.org/keywords/integer-factorization","display_name":"integer factorization","score":0.8270000219345093},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7149999737739563},{"id":"https://openalex.org/keywords/direct-products","display_name":"direct products","score":0.625},{"id":"https://openalex.org/keywords/direct-sums","display_name":"direct sums","score":0.7210000157356262},{"id":"https://openalex.org/keywords/exact-enumeration","display_name":"exact enumeration","score":0.4830000102519989},{"id":"https://openalex.org/keywords/combinatorial-enumeration","display_name":"combinatorial enumeration","score":0.5379999876022339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.741599977016449},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.7394999861717224},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6532999873161316},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5814999938011169},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5375000238418579},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4869999885559082},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4124000072479248},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.38760000467300415},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C191421660","wikidata":"https://www.wikidata.org/wiki/Q829546","display_name":"Primality test","level":3,"score":0.25949999690055847},{"id":"https://openalex.org/C52130261","wikidata":"https://www.wikidata.org/wiki/Q39825","display_name":"Census","level":3,"score":0.25130000710487366},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.25060001015663147}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2610.05617","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05617","pdf_url":"https://arxiv.org/pdf/2610.05617","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.2610.05617","doi":"https://doi.org/10.48550/arxiv.2610.05617","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05617","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"},{"id":"doi:10.5281/zenodo.23130296","doi":"https://doi.org/10.5281/zenodo.23130296","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23130296","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.23130297","doi":"https://doi.org/10.5281/zenodo.23130297","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23130297","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:2610.05617","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05617","pdf_url":"https://arxiv.org/pdf/2610.05617","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/W7219867474.pdf","grobid_xml":"https://content.openalex.org/works/W7219867474.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W1870348347","https://openalex.org/W1969990055","https://openalex.org/W1981139087","https://openalex.org/W1990300406","https://openalex.org/W1992901827","https://openalex.org/W2068115726","https://openalex.org/W2076500580","https://openalex.org/W2078986288","https://openalex.org/W2080342864","https://openalex.org/W2104994733","https://openalex.org/W2313098266","https://openalex.org/W2612992098","https://openalex.org/W2734132498","https://openalex.org/W2767220588","https://openalex.org/W2963181516","https://openalex.org/W4226246023","https://openalex.org/W4232306982","https://openalex.org/W4234956562","https://openalex.org/W4250204379","https://openalex.org/W4288804648","https://openalex.org/W4289785715","https://openalex.org/W4292958123","https://openalex.org/W4362679689","https://openalex.org/W4403662724","https://openalex.org/W4403704385","https://openalex.org/W4403775545","https://openalex.org/W4409864610","https://openalex.org/W4410219235","https://openalex.org/W6948072389","https://openalex.org/W7167621757","https://openalex.org/W7168295081","https://openalex.org/W7213473509","https://openalex.org/W7213586506"],"related_works":["https://openalex.org/W7221640575","https://openalex.org/W7221546656","https://openalex.org/W1994939255","https://openalex.org/W2059209074","https://openalex.org/W3063332968","https://openalex.org/W4313829291","https://openalex.org/W7099882304","https://openalex.org/W2979925312","https://openalex.org/W2073760267","https://openalex.org/W7099001473"],"abstract_inverted_index":{"Every":[0],"balanced":[1],"instance":[2],"of":[3,106,135],"the":[4,29,37,45,67,82,96,107,119,132,136,140,148],"stable":[5,79],"marriage":[6],"problem":[7],"with":[8,76,86,110],"strict":[9],"complete":[10],"preferences":[11],"has":[12],"a":[13,34,41,49,77,93,151,156],"unique":[14],"finest":[15],"partition":[16,23,141],"into":[17],"prime":[18,85,97],"blocks,":[19],"and":[20,44,55,81,118,147],"that":[21],"single":[22,78],"simultaneously":[24],"factors":[25],"three":[26],"different":[27],"structures:":[28],"reachable":[30],"execution":[31,70],"digraph":[32],"as":[33,40,48,131],"Cartesian":[35],"product,":[36],"proposal-prefix":[38],"antimatroid":[39],"direct":[42,50],"sum,":[43],"stable-matching":[46],"lattice":[47],"product.":[51],"The":[52,127],"converse":[53],"fails,":[54],"fails":[56],"at":[57,99],"every":[58,100],"size":[59],"from":[60],"two":[61,63],"on:":[62],"explicit":[64],"families":[65],"share":[66],"identical":[68],"Boolean-cube":[69],"while":[71],"one":[72],"is":[73,84,122,142,150],"maximally":[74],"decomposable":[75,117,120],"matching":[80],"other":[83],"n.":[87],"Uniqueness":[88],"yields":[89],"an":[90],"exact":[91],"census,":[92],"recursion":[94],"counting":[95],"instances":[98],"size,":[101],"under":[102],"which":[103],"exactly":[104],"88,478,208":[105],"110,075,314,176":[108],"profiles":[109],"four":[111],"agents":[112],"on":[113],"each":[114],"side":[115],"are":[116,129],"fraction":[121],"asymptotically":[123],"n!":[124],"/":[125],"n^(2n).":[126],"blocks":[128],"characterised":[130],"square":[133],"components":[134],"mutual-rank":[137],"filtration,":[138],"so":[139],"computable":[143],"in":[144],"polynomial":[145],"time":[146],"factorisation":[149],"tool":[152],"rather":[153],"than":[154],"only":[155],"fact.":[157]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-05T00:00:00"}
