{"id":"https://openalex.org/W2913038036","doi":"https://doi.org/10.1137/090775336","title":"Binary Nontiles","display_name":"Binary Nontiles","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2913038036","doi":"https://doi.org/10.1137/090775336","mag":"2913038036"},"language":"en","primary_location":{"id":"doi:10.1137/090775336","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775336","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":["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/A5067588072","display_name":"Don Coppersmith","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Don Coppersmith","raw_affiliation_strings":["victor@idaccr.org and dcopper@idaccr.org#TAB#"],"affiliations":[{"raw_affiliation_string":"victor@idaccr.org and dcopper@idaccr.org#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085804010","display_name":"Victor S. Miller","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Victor S. Miller","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5067588072"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.3477049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"1","first_page":"30","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9980999827384949,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9980999827384949,"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/T12029","display_name":"DNA and Biological Computing","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/tile","display_name":"Tile","score":0.8881525993347168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7420839667320251},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7173281311988831},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5349487066268921},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5145511031150818},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4899422526359558},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.48680374026298523},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.4623711109161377},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.43675482273101807},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.25665295124053955}],"concepts":[{"id":"https://openalex.org/C2780728851","wikidata":"https://www.wikidata.org/wiki/Q468402","display_name":"Tile","level":2,"score":0.8881525993347168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7420839667320251},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7173281311988831},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5349487066268921},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5145511031150818},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4899422526359558},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.48680374026298523},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.4623711109161377},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.43675482273101807},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.25665295124053955},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C153349607","wikidata":"https://www.wikidata.org/wiki/Q36649","display_name":"Visual arts","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/090775336","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775336","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1968245102","https://openalex.org/W1969744767","https://openalex.org/W2009917512","https://openalex.org/W2077278144","https://openalex.org/W2160658340","https://openalex.org/W2166015129","https://openalex.org/W2166966427"],"related_works":["https://openalex.org/W2384156839","https://openalex.org/W2114959296","https://openalex.org/W4321602641","https://openalex.org/W2394251275","https://openalex.org/W38346124","https://openalex.org/W4241392912","https://openalex.org/W2502442966","https://openalex.org/W2138666621","https://openalex.org/W2489497330","https://openalex.org/W2383936314"],"abstract_inverted_index":{"A":[0],"subset":[1,32],"$V":[2],"\\subseteq":[3,34],"\\mathbb{F}_2^n$":[4,35,40],"is":[5,22,30,86,101],"a":[6,23,31,45,74,87,103,111,121,129],"tile":[7,24,76],"if":[8,25,28],"$\\mathbb{F}_2^n$":[9],"can":[10],"be":[11],"covered":[12],"by":[13,135],"disjoint":[14],"translates":[15],"of":[16,110,120,131,151,161],"V.":[17],"In":[18,63,89],"other":[19],"words,":[20],"V":[21,77,100],"and":[26,53,59,69,78,114,138],"only":[27],"there":[29],"$A":[33],"such":[36],"that":[37,51,99,159],"$V+A":[38],"=":[39,46],"uniquely":[41],"(i.e.,":[42],"$v":[43],"+":[44,48],"v'":[47],"a'$":[49],"implies":[50],"$v=v'$":[52],"$a=a'$,":[54],"where":[55],"$v,v'":[56],"\\in":[57,61],"V$":[58],"$a,a'":[60],"A$).":[62],"some":[64],"problems":[65],"in":[66,148,164],"coding":[67],"theory":[68],"hashing":[70,152],"we":[71,92],"are":[72],"given":[73,134],"putative":[75,132],"wish":[79],"to":[80,128,153,157],"know":[81],"whether":[82],"or":[83],"not":[84,102],"it":[85],"tile.":[88,104],"this":[90],"paper":[91],"give":[93],"two":[94],"computational":[95],"criteria":[96,127],"for":[97],"certifying":[98],"The":[105],"first":[106],"involves":[107,117],"the":[108,115,118,149],"impossibility":[109],"bin-packing":[112],"problem,":[113],"second":[116],"infeasibility":[119],"linear":[122],"program.":[123],"We":[124],"apply":[125],"both":[126],"list":[130],"tiles":[133],"Gordon,":[136],"Miller,":[137],"Ostapenko":[139],"[IEEE":[140],"Trans.":[141],"Inform.":[142],"Theory,":[143],"56":[144],"(2010),":[145],"pp.":[146],"984\u2013991]":[147],"context":[150],"find":[154],"close":[155],"matches,":[156],"show":[158],"none":[160],"them":[162],"are,":[163],"fact,":[165],"tiles.":[166]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2019-02-21T00:00:00"}
