{"id":"https://openalex.org/W2787428120","doi":"https://doi.org/10.1137/16m110407x","title":"Counting Blanks in Polygonal Arrangements","display_name":"Counting Blanks in Polygonal Arrangements","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2787428120","doi":"https://doi.org/10.1137/16m110407x","mag":"2787428120"},"language":"en","primary_location":{"id":"doi:10.1137/16m110407x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m110407x","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":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1604.00960","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068567329","display_name":"Arseniy Akopyan","orcid":"https://orcid.org/0000-0002-2548-617X"},"institutions":[{"id":"https://openalex.org/I157556583","display_name":"Institute of Science and Technology Austria","ror":"https://ror.org/03gnh5541","country_code":"AT","type":"education","lineage":["https://openalex.org/I157556583"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Arseniy Akopyan","raw_affiliation_strings":["Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science and Technology Austria (IST Austria), Am Campus 1, 3400 Klosterneuburg, Austria","institution_ids":["https://openalex.org/I157556583"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085873807","display_name":"Erel Segal-Halevi","orcid":"https://orcid.org/0000-0002-7497-5834"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Erel Segal-Halevi","raw_affiliation_strings":["Ariel University (Ariel 40700) and Bar-Ilan University (Ramat-Gan 52900), Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ariel University (Ariel 40700) and Bar-Ilan University (Ramat-Gan 52900), Israel","institution_ids":["https://openalex.org/I52170813"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068567329"],"corresponding_institution_ids":["https://openalex.org/I157556583"],"apc_list":null,"apc_paid":null,"fwci":0.6031,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.748998,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"32","issue":"3","first_page":"2242","last_page":"2257"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.7213000059127808,"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":0.7213000059127808,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6708245873451233},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.659148097038269},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3946196436882019}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6708245873451233},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.659148097038269},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3946196436882019}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m110407x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m110407x","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:1604.00960","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.00960","pdf_url":"https://arxiv.org/pdf/1604.00960","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,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1604.00960","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1604.00960","pdf_url":"https://arxiv.org/pdf/1604.00960","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,"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":[],"awards":[{"id":"https://openalex.org/G1147446789","display_name":null,"funder_award_id":"1083/13","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G2488755638","display_name":null,"funder_award_id":"FP7/2007-2013","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"},{"id":"https://openalex.org/G3207356259","display_name":null,"funder_award_id":"2007\u20132013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G362819587","display_name":null,"funder_award_id":"291734","funder_id":"https://openalex.org/F4320334679","funder_display_name":"Research Executive Agency"},{"id":"https://openalex.org/G393177772","display_name":null,"funder_award_id":"FP7 2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5702163051","display_name":null,"funder_award_id":"FP7/2007","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6658030547","display_name":"International IST Postdoctoral Fellowship Programme","funder_award_id":"291734","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321449","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"},{"id":"https://openalex.org/F4320334679","display_name":"Research Executive Agency","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1427726556","https://openalex.org/W1906492141","https://openalex.org/W1994048022","https://openalex.org/W2609485929","https://openalex.org/W3023768696","https://openalex.org/W4301872252"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"Inside":[0],"a":[1,11],"two-dimensional":[2],"region":[3],"(``cake''),":[4],"there":[5],"are":[6,61,69,77,91],"$m$":[7],"nonoverlapping":[8],"tiles":[9],"of":[10,31,105],"certain":[12],"kind":[13],"(``toppings'').":[14],"We":[15,49],"want":[16],"to":[17],"expand":[18],"the":[19,32,38,89,103],"toppings":[20,60,68,76,90],"while":[21],"keeping":[22],"them":[23],"nonoverlapping,":[24],"and":[25,59,67,75,88],"possibly":[26],"add":[27],"some":[28],"blank":[29],"pieces":[30],"same":[33],"\u201ccertain":[34],"kind,\u201d":[35],"such":[36],"that":[37],"entire":[39],"cake":[40,58,66,74,82],"is":[41,83],"covered.":[42],"How":[43],"many":[44],"blanks":[45],"must":[46],"we":[47,98],"add?":[48],"study":[50],"this":[51],"question":[52],"in":[53],"several":[54],"cases:":[55],"(1)":[56],"The":[57,65,73,81],"general":[62],"polygons.":[63],"(2)":[64],"convex":[70],"figures.":[71],"(3)":[72],"axis-parallel":[78,85,92],"rectangles.":[79,93],"(4)":[80],"an":[84],"rectilinear":[86],"polygon":[87],"In":[94],"all":[95],"four":[96],"cases,":[97],"provide":[99],"tight":[100],"bounds":[101],"on":[102],"number":[104],"blanks.":[106]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
