{"id":"https://openalex.org/W1522918325","doi":"https://doi.org/10.37236/1857","title":"Filling a Box with Translates of Two Bricks","display_name":"Filling a Box with Translates of Two Bricks","publication_year":2004,"publication_date":"2004-12-07","ids":{"openalex":"https://openalex.org/W1522918325","doi":"https://doi.org/10.37236/1857","mag":"1522918325"},"language":"en","primary_location":{"id":"doi:10.37236/1857","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1857","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1n16/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1n16/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037218234","display_name":"Mihail N. Kolountzakis","orcid":"https://orcid.org/0000-0001-9598-4580"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]}],"countries":["GR","US"],"is_corresponding":true,"raw_author_name":"Mihail N. Kolountzakis","raw_affiliation_strings":["Department of Mathematics, University of Crete, Knossos Ave., 714 09 Iraklio, Greece","School of Mathematics, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, GA 30332, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Crete, Knossos Ave., 714 09 Iraklio, Greece","institution_ids":["https://openalex.org/I142617266"]},{"raw_affiliation_string":"School of Mathematics, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037218234"],"corresponding_institution_ids":["https://openalex.org/I130701444","https://openalex.org/I142617266"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.06059101,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9959999918937683,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9945999979972839,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/brick","display_name":"Brick","score":0.8706493377685547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6697112917900085},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4302443861961365},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37663814425468445},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16824975609779358},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.05929449200630188}],"concepts":[{"id":"https://openalex.org/C154226666","wikidata":"https://www.wikidata.org/wiki/Q40089","display_name":"Brick","level":2,"score":0.8706493377685547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6697112917900085},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4302443861961365},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37663814425468445},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16824975609779358},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.05929449200630188},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1857","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1857","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1n16/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.235.7466","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.235.7466","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0409381v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.66.4415","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.66.4415","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PostScriptfiles/v11i1n16.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.74.1429","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.74.1429","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PDF/v11i1n16.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.98.1500","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.98.1500","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://fourier.math.uoc.gr/~mk/ps/bricks.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1857","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1857","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1n16/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6800000071525574,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G4447653093","display_name":null,"funder_award_id":"Network","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1522918325.pdf","grobid_xml":"https://content.openalex.org/works/W1522918325.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1602518544","https://openalex.org/W2121848728"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2383709437","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2730245355","https://openalex.org/W1587224694"],"abstract_inverted_index":{"We":[0,42,81],"give":[1],"a":[2,17],"new":[3],"proof":[4,75],"of":[5,26,29,49,56,92,97],"the":[6,39,45,62,67,71,78],"following":[7,40],"interesting":[8],"fact":[9],"recently":[10],"proved":[11],"by":[12],"Bower":[13],"and":[14,66],"Michael:":[15],"if":[16],"$d$-dimensional":[18],"rectangular":[19,30],"box":[20,46],"can":[21,34,43,58],"be":[22,36,59],"tiled":[23,37,60],"using":[24],"translates":[25,91],"two":[27,53,95],"types":[28,96],"bricks,":[31],"then":[32],"it":[33],"also":[35,82],"in":[38],"way.":[41],"cut":[44],"across":[47],"one":[48,55,69],"its":[50],"sides":[51],"into":[52],"boxes,":[54],"which":[57],"with":[61,70],"first":[63],"brick":[64],"only":[65],"other":[68],"second":[72],"brick.":[73],"Our":[74],"relies":[76],"on":[77],"Fourier":[79],"Transform.":[80],"show":[83],"that":[84],"no":[85],"such":[86],"result":[87],"is":[88],"true":[89],"for":[90],"more":[93],"than":[94],"bricks.":[98]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}