{"id":"https://openalex.org/W7214997529","doi":"https://doi.org/10.48550/arxiv.2609.37159","title":"An equivalent form of Hindman's Theorem","display_name":"An equivalent form of Hindman's Theorem","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214997529","doi":"https://doi.org/10.48550/arxiv.2609.37159"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37159","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37159","pdf_url":"https://arxiv.org/pdf/2609.37159","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/2609.37159","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038321878","display_name":"Lorenzo Carlucci","orcid":"https://orcid.org/0000-0001-8238-0315","observed_orcids":["https://orcid.org/0000-0001-8238-0315"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Carlucci, Lorenzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5032154488","display_name":"Andrea D\u2019Amico","orcid":"https://orcid.org/0000-0003-0828-6157","observed_orcids":["https://orcid.org/0000-0003-0828-6157"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D'Amico, Andrea","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.7031000256538391,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.7031000256538391,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.1720999926328659,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.01720000058412552,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hindman-s-theorem","display_name":"Hindman's theorem","score":0.9229999780654907},{"id":"https://openalex.org/keywords/ramsey-s-theorem","display_name":"Ramsey's theorem","score":0.984000027179718},{"id":"https://openalex.org/keywords/ramsey-theory","display_name":"Ramsey theory","score":0.5440000295639038},{"id":"https://openalex.org/keywords/ultrafilters","display_name":"ultrafilters","score":0.6209999918937683},{"id":"https://openalex.org/keywords/combinatorial-number-theory","display_name":"combinatorial number theory","score":0.6499999761581421},{"id":"https://openalex.org/keywords/equivalence-of-theorems","display_name":"equivalence of theorems","score":0.6240000128746033}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7975000143051147},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5400999784469604},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4465000033378601},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.375},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.35339999198913574},{"id":"https://openalex.org/C146147875","wikidata":"https://www.wikidata.org/wiki/Q1144897","display_name":"Brouwer fixed-point theorem","level":3,"score":0.35089999437332153},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C171636804","wikidata":"https://www.wikidata.org/wiki/Q1149458","display_name":"Compactness theorem","level":4,"score":0.3294999897480011},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3260999917984009},{"id":"https://openalex.org/C2776230367","wikidata":"https://www.wikidata.org/wiki/Q7314222","display_name":"Representation theorem","level":2,"score":0.31529998779296875},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.30000001192092896},{"id":"https://openalex.org/C48540410","wikidata":"https://www.wikidata.org/wiki/Q5221089","display_name":"Danskin's theorem","level":4,"score":0.2948000133037567},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2937000095844269},{"id":"https://openalex.org/C90985795","wikidata":"https://www.wikidata.org/wiki/Q5042898","display_name":"Carlson's theorem","level":5,"score":0.27059999108314514},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C119050217","wikidata":"https://www.wikidata.org/wiki/Q17101806","display_name":"Intersection theorem","level":5,"score":0.266400009393692},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2581999897956848},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C139588767","wikidata":"https://www.wikidata.org/wiki/Q17098096","display_name":"Mean value theorem (divided differences)","level":4,"score":0.2556999921798706}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37159","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37159","pdf_url":"https://arxiv.org/pdf/2609.37159","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.2609.37159","doi":"https://doi.org/10.48550/arxiv.2609.37159","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37159","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:2609.37159","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37159","pdf_url":"https://arxiv.org/pdf/2609.37159","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/W7214997529.pdf","grobid_xml":"https://content.openalex.org/works/W7214997529.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W2598488631"],"related_works":["https://openalex.org/W2769392855","https://openalex.org/W2225409823","https://openalex.org/W2950651278","https://openalex.org/W2964266688","https://openalex.org/W2047891343","https://openalex.org/W2582449216","https://openalex.org/W1983956520","https://openalex.org/W3037190989","https://openalex.org/W2557435570","https://openalex.org/W2952476743"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2],"equivalence":[3],"of":[4,13],"Hindman's":[5],"finite":[6],"sums":[7],"theorem":[8],"with":[9],"a":[10],"natural":[11],"extension":[12],"Ramsey's":[14],"theorem.":[15]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}