{"id":"https://openalex.org/W7118849104","doi":"https://doi.org/10.1007/s00493-025-00195-7","title":"The complex Illumination problem","display_name":"The complex Illumination problem","publication_year":2026,"publication_date":"2026-01-07","ids":{"openalex":"https://openalex.org/W7118849104","doi":"https://doi.org/10.1007/s00493-025-00195-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-025-00195-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00195-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00195-7.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00195-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047099826","display_name":"Liran Rotem","orcid":"https://orcid.org/0000-0003-1512-7277"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Liran Rotem","raw_affiliation_strings":["Faculty of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114337198","display_name":"Alon Schejter","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Alon Schejter","raw_affiliation_strings":["Faculty of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technion - Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012258033","display_name":"Boaz A. Slomka","orcid":"https://orcid.org/0000-0003-1387-1940"},"institutions":[{"id":"https://openalex.org/I164950643","display_name":"Open University of Israel","ror":"https://ror.org/027z64205","country_code":"IL","type":"education","lineage":["https://openalex.org/I164950643"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Boaz A. Slomka","raw_affiliation_strings":["Department of Mathematics and Computer Science, The Open University of Israel, Ra\u2019anana, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, The Open University of Israel, Ra\u2019anana, Israel","institution_ids":["https://openalex.org/I164950643"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5047099826"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05471882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"46","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.7052000164985657,"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":0.7052000164985657,"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/T11822","display_name":"Analytic and geometric function theory","score":0.049800001084804535,"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/T10884","display_name":"Holomorphic and Operator Theory","score":0.046300001442432404,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polydisc","display_name":"Polydisc","score":0.864799976348877},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6927000284194946},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5692999958992004},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.4124999940395355},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.37439998984336853},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.31360000371932983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8694999814033508},{"id":"https://openalex.org/C88324339","wikidata":"https://www.wikidata.org/wiki/Q2103196","display_name":"Polydisc","level":3,"score":0.864799976348877},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5692999958992004},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5077999830245972},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31220000982284546},{"id":"https://openalex.org/C110202963","wikidata":"https://www.wikidata.org/wiki/Q1783542","display_name":"Convex geometry","level":5,"score":0.3107999861240387},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C9417928","wikidata":"https://www.wikidata.org/wiki/Q1070689","display_name":"Image processing","level":3,"score":0.2526000142097473},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25200000405311584},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2515999972820282},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-025-00195-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00195-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00195-7.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00493-025-00195-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00195-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00195-7.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3629486451","display_name":null,"funder_award_id":"784/20","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G4127838089","display_name":null,"funder_award_id":"NSF-BSF","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5807727555","display_name":"NNA Track 2: PredictFest: To Build Capacity for Arctic Stakeholders in Need of Multi-Scale Predictions","funder_award_id":"2022707","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"},{"id":"https://openalex.org/F4320317241","display_name":"Open University of Israel","ror":"https://ror.org/027z64205"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7118849104.pdf"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W360428934","https://openalex.org/W621995200","https://openalex.org/W788409157","https://openalex.org/W1540748742","https://openalex.org/W1549191761","https://openalex.org/W1596900230","https://openalex.org/W1807179603","https://openalex.org/W1968750047","https://openalex.org/W1969836943","https://openalex.org/W1985709807","https://openalex.org/W1993604621","https://openalex.org/W2007622853","https://openalex.org/W2008351584","https://openalex.org/W2011877429","https://openalex.org/W2017008566","https://openalex.org/W2020353244","https://openalex.org/W2027107806","https://openalex.org/W2034423930","https://openalex.org/W2039486702","https://openalex.org/W2041222127","https://openalex.org/W2041947933","https://openalex.org/W2044374917","https://openalex.org/W2049798553","https://openalex.org/W2054236010","https://openalex.org/W2055666178","https://openalex.org/W2061395994","https://openalex.org/W2067513565","https://openalex.org/W2071303594","https://openalex.org/W2079557312","https://openalex.org/W2089322337","https://openalex.org/W2111185360","https://openalex.org/W2113672731","https://openalex.org/W2120086061","https://openalex.org/W2122146382","https://openalex.org/W2123253959","https://openalex.org/W2139885592","https://openalex.org/W2150353076","https://openalex.org/W2155549190","https://openalex.org/W2161630387","https://openalex.org/W2166719346","https://openalex.org/W2316934731","https://openalex.org/W2321084059","https://openalex.org/W2473782729","https://openalex.org/W2490745741","https://openalex.org/W2911873805","https://openalex.org/W2963427638","https://openalex.org/W2963456899","https://openalex.org/W2964093814","https://openalex.org/W2969634849","https://openalex.org/W2972778548","https://openalex.org/W2982607135","https://openalex.org/W3101332897","https://openalex.org/W3120597765","https://openalex.org/W3193029973","https://openalex.org/W4286652367","https://openalex.org/W4293203915","https://openalex.org/W4317035214","https://openalex.org/W4385886815","https://openalex.org/W4386582663","https://openalex.org/W4387097806","https://openalex.org/W4394565605","https://openalex.org/W4403753944","https://openalex.org/W4413186460","https://openalex.org/W4413186473","https://openalex.org/W4413888283"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,63],"formulate":[2],"a":[3],"complex":[4,15,55,146],"analog":[5,56],"of":[6,53,57,69,109,145],"the":[7,47,54,58,61,66,70,105,110,143],"celebrated":[8],"Levi-Hadwiger-Boltyanski":[9],"illumination":[10,51,67,107],"(or":[11],"covering)":[12],"conjecture":[13],"for":[14,142],"convex":[16],"bodies":[17],"in":[18,41,72,112],"$$\\mathbb":[19,73,113],"{C}^n$$":[20,74,114],"<mml:math":[21,75,88,115,128],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[22,76,89,116,129],"<mml:msup>":[23,77,91,117,130],"<mml:mrow>":[24,78,90,93,118],"<mml:mi>C</mml:mi>":[25,79,119],"</mml:mrow>":[26,80,97,101,120],"<mml:mi>n</mml:mi>":[27,81,94,121,132],"</mml:msup>":[28,82,98,122,133],"</mml:math>":[29,83,102,123,134],",":[30],"as":[31,33],"well":[32],"its":[34],"(non-comparable)":[35],"fractional":[36,50,106],"version.":[37],"A":[38],"key":[39],"element":[40],"posing":[42],"these":[43],"problems":[44],"is":[45,84,124],"computing":[46],"classical":[48],"and":[49,103,148],"numbers":[52],"hypercube,":[59],"i.e.,":[60],"polydisc.":[62],"prove":[64],"that":[65,104],"number":[68,108],"polydisc":[71,111],"equal":[85,125],"to":[86,126],"$$2^{n+1}-1$$":[87],"<mml:mn>2</mml:mn>":[92,131],"<mml:mo>+</mml:mo>":[95],"<mml:mn>1</mml:mn>":[96,100],"<mml:mo>-</mml:mo>":[99],"$$2^n$$":[127],".":[135],"In":[136],"addition,":[137],"we":[138],"verify":[139],"both":[140],"conjectures":[141],"classes":[144],"zonotopes":[147],"zonoids.":[149]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2026-01-08T00:00:00"}