{"id":"https://openalex.org/W3082231509","doi":"https://doi.org/10.1137/20m1365119","title":"A M\u00e9lange of Diameter Helly-Type Theorems","display_name":"A M\u00e9lange of Diameter Helly-Type Theorems","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3082231509","doi":"https://doi.org/10.1137/20m1365119","mag":"3082231509"},"language":"en","primary_location":{"id":"doi:10.1137/20m1365119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1365119","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2008.13737","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070223858","display_name":"Travis Dillon","orcid":"https://orcid.org/0000-0002-4250-8836"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Travis Dillon","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5058480137","display_name":"Pablo Sober\u00f3n","orcid":"https://orcid.org/0000-0003-2347-4279"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pablo Sober\u00f3n","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070223858"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.02559063,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"35","issue":"3","first_page":"1615","last_page":"1627"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.9919999837875366,"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/mathematics","display_name":"Mathematics","score":0.7774368524551392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7473818063735962},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5750367045402527},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5460344552993774},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5367300510406494},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5124945640563965},{"id":"https://openalex.org/keywords/unit-sphere","display_name":"Unit sphere","score":0.5113153457641602},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4276576638221741},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.4234391748905182},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3428196907043457},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1363247036933899},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07041433453559875}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7774368524551392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7473818063735962},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5750367045402527},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5460344552993774},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5367300510406494},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5124945640563965},{"id":"https://openalex.org/C191948623","wikidata":"https://www.wikidata.org/wiki/Q1307800","display_name":"Unit sphere","level":2,"score":0.5113153457641602},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4276576638221741},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.4234391748905182},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3428196907043457},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1363247036933899},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07041433453559875},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1365119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1365119","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2008.13737","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.13737","pdf_url":"https://arxiv.org/pdf/2008.13737","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3082231509","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2008.13737.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2008.13737","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2008.13737","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2008.13737","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.13737","pdf_url":"https://arxiv.org/pdf/2008.13737","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2709322963","display_name":null,"funder_award_id":"DMS-1851420","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6436102805","display_name":null,"funder_award_id":"DMS-1802059","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7970203726","display_name":null,"funder_award_id":"DMS-1953141","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3082231509.pdf","grobid_xml":"https://content.openalex.org/works/W3082231509.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W107540463","https://openalex.org/W1509442273","https://openalex.org/W1553598118","https://openalex.org/W1947254580","https://openalex.org/W1972671995","https://openalex.org/W1984879308","https://openalex.org/W1992399294","https://openalex.org/W2016830182","https://openalex.org/W2020592712","https://openalex.org/W2041512616","https://openalex.org/W2049652998","https://openalex.org/W2053369489","https://openalex.org/W2062068855","https://openalex.org/W2066037950","https://openalex.org/W2094116098","https://openalex.org/W2174692193","https://openalex.org/W2254628246","https://openalex.org/W2285444140","https://openalex.org/W2299064519","https://openalex.org/W2301339721","https://openalex.org/W2551850732","https://openalex.org/W2761160398","https://openalex.org/W2763349972","https://openalex.org/W2963281405","https://openalex.org/W2963846517","https://openalex.org/W2963886109","https://openalex.org/W2963928068","https://openalex.org/W2967115303","https://openalex.org/W3035918817","https://openalex.org/W3036236415","https://openalex.org/W3105314861","https://openalex.org/W3147016942","https://openalex.org/W3161818435","https://openalex.org/W3200473192","https://openalex.org/W4251668038"],"related_works":["https://openalex.org/W2237746464","https://openalex.org/W2285444140","https://openalex.org/W3161818435","https://openalex.org/W589602860","https://openalex.org/W3112970936","https://openalex.org/W1900214672","https://openalex.org/W2299064519","https://openalex.org/W2045244608","https://openalex.org/W2081708716","https://openalex.org/W2963846517","https://openalex.org/W2091534093","https://openalex.org/W2504636406","https://openalex.org/W2809169079","https://openalex.org/W2761160398","https://openalex.org/W2301339721","https://openalex.org/W2074581052","https://openalex.org/W2799216784","https://openalex.org/W2012314757","https://openalex.org/W2008582047","https://openalex.org/W3100551532"],"abstract_inverted_index":{"A":[0],"Helly-type":[1,62,88],"theorem":[2,63],"for":[3,64,81,90],"diameter":[4,10,28,65],"provides":[5],"a":[6,15,44,56,74,78],"bound":[7],"on":[8,26],"the":[9,12,27,30,91],"of":[11,14,18,29,32,43,93],"intersection":[13,31],"finite":[16],"family":[17],"convex":[19],"sets":[20],"in":[21],"$\\mathbb{R}^d$":[22],"given":[23],"some":[24],"information":[25],"all":[33],"sufficiently":[34],"small":[35],"subfamilies.":[36],"We":[37,52],"prove":[38,77,87],"fractional":[39],"and":[40,50,67,76],"colorful":[41,79],"versions":[42],"long-standing":[45],"conjecture":[46],"by":[47],"B\u00e1r\u00e1ny,":[48],"Katchalski,":[49],"Pach.":[51],"also":[53],"show":[54],"that":[55,83],"Minkowski":[57],"norm":[58],"admits":[59],"an":[60],"exact":[61],"if":[66,69],"only":[68],"its":[70],"unit":[71],"ball":[72],"is":[73],"polytope":[75],"version":[80],"those":[82],"do.":[84],"Finally,":[85],"we":[86],"theorems":[89],"property":[92],"\u201ccontaining":[94],"$k$":[95],"colinear":[96],"integer":[97],"points.\u201d":[98]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}