{"id":"https://openalex.org/W2041443188","doi":"https://doi.org/10.1145/2462356.2462369","title":"Equal coefficients and tolerance in coloured tverberg partitions","display_name":"Equal coefficients and tolerance in coloured tverberg partitions","publication_year":2013,"publication_date":"2013-06-17","ids":{"openalex":"https://openalex.org/W2041443188","doi":"https://doi.org/10.1145/2462356.2462369","mag":"2041443188"},"language":"en","primary_location":{"id":"doi:10.1145/2462356.2462369","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2462356.2462369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-ninth annual symposium on Computational geometry","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058480137","display_name":"Pablo Sober\u00f3n","orcid":"https://orcid.org/0000-0003-2347-4279"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Pablo Sober\u00f3n","raw_affiliation_strings":["University College London, London, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University College London, London, United Kingdom","institution_ids":["https://openalex.org/I45129253"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058480137"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":null,"apc_paid":null,"fwci":1.5067,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.76646707,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"91","last_page":"96"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9883000254631042,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9883000254631042,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9767000079154968,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9247000217437744,"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/combinatorics","display_name":"Combinatorics","score":0.8463938236236572},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.7661641836166382},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6321313381195068},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6316351294517517},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5530571937561035},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5404989719390869},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.4837746322154999},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.412075400352478},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36226344108581543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19907143712043762},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13989192247390747},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08773908019065857}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8463938236236572},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.7661641836166382},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6321313381195068},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6316351294517517},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5530571937561035},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5404989719390869},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4837746322154999},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.412075400352478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36226344108581543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19907143712043762},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13989192247390747},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08773908019065857}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/2462356.2462369","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2462356.2462369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twenty-ninth annual symposium on Computational geometry","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1493018669","https://openalex.org/W1967139274","https://openalex.org/W1971444741","https://openalex.org/W1977098616","https://openalex.org/W1984879308","https://openalex.org/W1990498689","https://openalex.org/W1996168654","https://openalex.org/W2004331157","https://openalex.org/W2007366961","https://openalex.org/W2013540964","https://openalex.org/W2027584441","https://openalex.org/W2046487802","https://openalex.org/W2048784051","https://openalex.org/W2049652998","https://openalex.org/W2051428257","https://openalex.org/W2069358690","https://openalex.org/W2076053977","https://openalex.org/W2109256783","https://openalex.org/W2110134123","https://openalex.org/W2120948000","https://openalex.org/W2132220587","https://openalex.org/W2141867510","https://openalex.org/W2147282740","https://openalex.org/W2150986573","https://openalex.org/W2162144048","https://openalex.org/W2963084798","https://openalex.org/W2964266200","https://openalex.org/W4285719527","https://openalex.org/W6676442648"],"related_works":["https://openalex.org/W2363904277","https://openalex.org/W1982962927","https://openalex.org/W2128601753","https://openalex.org/W2048874717","https://openalex.org/W2372035979","https://openalex.org/W2393489669","https://openalex.org/W3161249280","https://openalex.org/W2375652826","https://openalex.org/W2267059662","https://openalex.org/W1987507258"],"abstract_inverted_index":{"The":[0],"coloured":[1],"Tverberg":[2],"theorem":[3],"was":[4],"conjectured":[5],"by":[6],"Barany,":[7],"Lovasz":[8],"and":[9,12,65,160],"Furedi":[10],"[2]":[11],"asks":[13],"whether":[14],"for":[15],"any":[16,108],"d+1":[17],"sets":[18,38,77,101,134],"(considered":[19],"as":[20],"colour":[21,61,112,119,147],"classes)":[22],"of":[23,33,98,110,121,129,144,156,168],"k":[24,36,132],"points":[25],"each":[26,85],"in":[27,70,74,84],"Rd":[28],"there":[29,125],"is":[30,44,51,126],"a":[31,127],"partition":[32,128],"them":[34,130],"into":[35,131],"colourful":[37,76,100,133],"whose":[39],"convex":[40,72,96],"hulls":[41,97],"intersect.":[42],"This":[43],"known":[45],"when":[46],"d=1,2":[47],"[3]":[48],"or":[49],"k+1":[50],"prime":[52],"[5].":[53],"In":[54],"this":[55],"paper":[56],"we":[57,93,106,116],"show":[58,166],"that":[59,136],"(k-1)d+1":[60],"classes":[62,120,148],"are":[63,78,149],"necessary":[64],"sufficient":[66],"if":[67,92,105,115],"the":[68,71,75,82,95,99,111,140,154,157,161],"coefficients":[69,142],"combination":[73],"required":[79],"to":[80,102,171],"be":[81],"same":[83,141],"class.":[86],"We":[87,151,164],"also":[88,152],"examine":[89],"what":[90],"happens":[91],"want":[94],"intersect":[103,138],"even":[104],"remove":[107],"r":[109,146],"classes.":[113],"Namely,":[114],"have":[117],"(r+1)(k-1)d+1":[118],"$k$":[122],"point":[123],"each,":[124],"such":[135],"they":[137],"using":[139],"regardless":[143],"which":[145],"removed.":[150],"investigate":[153],"relation":[155],"case":[158],"k=2":[159],"Gale":[162],"transform.":[163],"then":[165],"applications":[167],"these":[169],"results":[170],"purely":[172],"combinatorial":[173],"problems.":[174]},"counts_by_year":[{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
