{"id":"https://openalex.org/W2301339721","doi":"https://doi.org/10.1007/s00454-016-9858-3","title":"Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets","display_name":"Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets","publication_year":2017,"publication_date":"2017-01-12","ids":{"openalex":"https://openalex.org/W2301339721","doi":"https://doi.org/10.1007/s00454-016-9858-3","mag":"2301339721"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-016-9858-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-016-9858-3","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","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/A5055755657","display_name":"Jes\u00fas A. De Loera","orcid":"https://orcid.org/0000-0002-9556-1112"},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jesus A. De Loera","raw_affiliation_strings":["Department of Mathematics, University of California, Davis, Davis, CA, 95616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Davis, Davis, CA, 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026221222","display_name":"R. N. La Haye","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Reuben N. La Haye","raw_affiliation_strings":["Department of Mathematics, University of California, Davis, Davis, CA, 95616, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Davis, Davis, CA, 95616, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056513353","display_name":"David Rolnick","orcid":"https://orcid.org/0000-0002-2855-393X"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Rolnick","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058480137","display_name":"Pablo Sober\u00f3n","orcid":"https://orcid.org/0000-0003-2347-4279"},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pablo Sober\u00f3n","raw_affiliation_strings":["Department of Mathematics, Northeastern University, Boston, MA, 02115, USA"],"raw_orcid":"https://orcid.org/0000-0003-2347-4279","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northeastern University, Boston, MA, 02115, USA","institution_ids":["https://openalex.org/I12912129"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5058480137"],"corresponding_institution_ids":["https://openalex.org/I12912129"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.851,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.89748169,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"58","issue":"2","first_page":"435","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998999834060669,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11106","display_name":"Data Management and Algorithms","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"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/mathematics","display_name":"Mathematics","score":0.8175764679908752},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7283220291137695},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7230981588363647},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7033544778823853},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.6762105226516724},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6146490573883057},{"id":"https://openalex.org/keywords/discrete-geometry","display_name":"Discrete geometry","score":0.6127474308013916},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.6067030429840088},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39615851640701294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13351866602897644}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8175764679908752},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7283220291137695},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7230981588363647},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7033544778823853},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.6762105226516724},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6146490573883057},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.6127474308013916},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.6067030429840088},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39615851640701294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13351866602897644},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-016-9858-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-016-9858-3","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org/ark:/13030/qt2037z49w","is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/2037z49w","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete and Computational Geometry, vol 58, iss 2","raw_type":"article"},{"id":"pmh:qt2037z49w","is_oa":false,"landing_page_url":"http://www.escholarship.org/uc/item/2037z49w","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"De Loera, JA; La Haye, RN; Rolnick, D; &amp; Sober\u00f3n, P. (2017). Quantitative Tverberg Theorems Over Lattices and Other Discrete Sets. Discrete and Computational Geometry, 58(2), 435 - 448. doi: 10.1007/s00454-016-9858-3. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/2037z49w","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2813472838","display_name":null,"funder_award_id":"1122374","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G8467107387","display_name":null,"funder_award_id":"1321794","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308797","display_name":"University of California Institute for Mexico and the United States","ror":"https://ror.org/03nawhv43"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W107506616","https://openalex.org/W107540463","https://openalex.org/W116606405","https://openalex.org/W136694183","https://openalex.org/W774919633","https://openalex.org/W1509442273","https://openalex.org/W1550662968","https://openalex.org/W1859614188","https://openalex.org/W1947254580","https://openalex.org/W1957600665","https://openalex.org/W1966931715","https://openalex.org/W1967257095","https://openalex.org/W1977098616","https://openalex.org/W1984879308","https://openalex.org/W1986429143","https://openalex.org/W1987752344","https://openalex.org/W1992399294","https://openalex.org/W1994709142","https://openalex.org/W2004331157","https://openalex.org/W2007366961","https://openalex.org/W2009545408","https://openalex.org/W2011116511","https://openalex.org/W2041512616","https://openalex.org/W2049652998","https://openalex.org/W2066037950","https://openalex.org/W2094116098","https://openalex.org/W2110134123","https://openalex.org/W2167816765","https://openalex.org/W2199978563","https://openalex.org/W2212143440","https://openalex.org/W2278042759","https://openalex.org/W2299064519","https://openalex.org/W2347587365","https://openalex.org/W2415114898","https://openalex.org/W2963846964","https://openalex.org/W3039948875","https://openalex.org/W4235730211","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W1996614773","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W2029391962","https://openalex.org/W1784887654"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
