{"id":"https://openalex.org/W7215742397","doi":"https://doi.org/10.48550/arxiv.2610.03851","title":"An Improved Upper Bound for Recovering Pairs","display_name":"An Improved Upper Bound for Recovering Pairs","publication_year":2026,"publication_date":"2026-10-02","ids":{"openalex":"https://openalex.org/W7215742397","doi":"https://doi.org/10.48550/arxiv.2610.03851"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.03851","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03851","pdf_url":"https://arxiv.org/pdf/2610.03851","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/2610.03851","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5126735187","display_name":"Simone Costa","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Costa, Simone","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5126735187"],"corresponding_institution_ids":["https://openalex.org/I79940851"],"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9740999937057495,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9740999937057495,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.023399999365210533,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.0003000000142492354,"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/hypergraphs","display_name":"hypergraphs","score":0.6299999952316284},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.5450000166893005},{"id":"https://openalex.org/keywords/entropy-inequality","display_name":"entropy inequality","score":0.8939999938011169},{"id":"https://openalex.org/keywords/convex-combination","display_name":"convex combination","score":0.640999972820282},{"id":"https://openalex.org/keywords/extremal-set-theory","display_name":"extremal set theory","score":0.7730000019073486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7997000217437744},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7621999979019165},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7508999705314636},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5511000156402588},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5090000033378601},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4034000039100647},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.39579999446868896},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.3783000111579895},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.2897000014781952},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.26109999418258667}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:2610.03851","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03851","pdf_url":"https://arxiv.org/pdf/2610.03851","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.2610.03851","doi":"https://doi.org/10.48550/arxiv.2610.03851","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.03851","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.23093259","doi":"https://doi.org/10.5281/zenodo.23093259","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23093259","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.23093260","doi":"https://doi.org/10.5281/zenodo.23093260","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23093260","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:2610.03851","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.03851","pdf_url":"https://arxiv.org/pdf/2610.03851","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7215742397.pdf","grobid_xml":"https://content.openalex.org/works/W7215742397.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1888933272","https://openalex.org/W1987305997","https://openalex.org/W2077246013","https://openalex.org/W2106100363","https://openalex.org/W2742527365","https://openalex.org/W3080579097","https://openalex.org/W3158439805","https://openalex.org/W4415995294","https://openalex.org/W7206158364","https://openalex.org/W7212044638"],"related_works":["https://openalex.org/W4302371224","https://openalex.org/W4415995294","https://openalex.org/W7206158364","https://openalex.org/W2742527365","https://openalex.org/W7097864790","https://openalex.org/W7212044638","https://openalex.org/W3149009238","https://openalex.org/W2070072395","https://openalex.org/W2045682744","https://openalex.org/W2786115592"],"abstract_inverted_index":{"We":[0,42],"prove":[1],"that":[2],"every":[3],"recovering":[4,40,59],"pair":[5,74],"$(\\mathcal{A},\\mathcal{B})$":[6],"of":[7,10,12,19,30,78],"nonempty":[8],"families":[9,69],"subsets":[11],"an":[13],"$n$-element":[14],"set":[15],"satisfies\\[":[16],"|\\mathcal{A}||\\mathcal{B}|\\le\\left(\\frac{223949}{100000}\\right)^n=(2.23949)^n.\\]A":[17],"result":[18],"Mond,":[20,79],"Souza":[21,80],"and":[22,32,81],"Versteegen,":[23],"combined":[24,88],"with":[25],"the":[26,58,62,65,72],"sharp":[27],"$(9/4)^n$":[28],"bound":[29,67],"Fang":[31],"Huang":[33],"for":[34,39],"cancellative":[35],"pairs,":[36],"gives":[37],"$(2.2499)^n$":[38],"pairs.":[41],"improve":[43],"this":[44],"to":[45,68],"$(2.23949)^n$.":[46],"The":[47,83],"proof":[48],"combines":[49],"two":[50,84],"entropy":[51],"inequalities.":[52],"One":[53],"is":[54],"derived":[55],"directly":[56],"from":[57,71],"property,":[60],"while":[61],"other":[63],"applies":[64],"Fang-Huang":[66],"obtained":[70],"original":[73],"by":[75,89],"a":[76,90],"construction":[77],"Versteegen.":[82],"inequalities":[85],"are":[86],"then":[87],"convex":[91],"combination.":[92]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-03T00:00:00"}
