{"id":"https://openalex.org/W1517833289","doi":"https://doi.org/10.37236/1462","title":"Rhombus Tilings of a Hexagon with Two Triangles Missing on the Symmetry Axis","display_name":"Rhombus Tilings of a Hexagon with Two Triangles Missing on the Symmetry Axis","publication_year":1999,"publication_date":"1999-07-27","ids":{"openalex":"https://openalex.org/W1517833289","doi":"https://doi.org/10.37236/1462","mag":"1517833289"},"language":"en","primary_location":{"id":"doi:10.37236/1462","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1462","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r30/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r30/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010246985","display_name":"Theresia Eisenk\u00f6lbl","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Theresia Eisenk\u00f6lbl","raw_affiliation_strings":["Univ. of Vienna#TAB#"],"affiliations":[{"raw_affiliation_string":"Univ. of Vienna#TAB#","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010246985"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":3.2865,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.9071357,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"6","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9997000098228455,"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":0.9997000098228455,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9987000226974487,"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/rhombus","display_name":"Rhombus","score":0.9653835296630859},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8054783344268799},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7594799995422363},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6775428056716919},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.4853002429008484},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.26310762763023376},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23685172200202942}],"concepts":[{"id":"https://openalex.org/C161903591","wikidata":"https://www.wikidata.org/wiki/Q41159","display_name":"Rhombus","level":2,"score":0.9653835296630859},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8054783344268799},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7594799995422363},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6775428056716919},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4853002429008484},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.26310762763023376},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23685172200202942}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/1462","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1462","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r30/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":false,"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:10.1.1.239.7756","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7756","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/9810019v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.45.9044","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.9044","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_6/../Volume_6/PostScriptfiles/v6i1r30.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.665","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.665","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ethz.ch/EMIS/journals/EJC/Volume_6/PDF/v6i1r30.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1462","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1462","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v6i1r30/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":false,"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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1517833289.pdf","grobid_xml":"https://content.openalex.org/works/W1517833289.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W47205671","https://openalex.org/W1842498742","https://openalex.org/W1967472879","https://openalex.org/W2001969070","https://openalex.org/W2039134431","https://openalex.org/W2328425686","https://openalex.org/W2794407181","https://openalex.org/W6636007523","https://openalex.org/W6682324371"],"related_works":["https://openalex.org/W3164467166","https://openalex.org/W4379389000","https://openalex.org/W1970378093","https://openalex.org/W2584375338","https://openalex.org/W1552842083","https://openalex.org/W2951995717","https://openalex.org/W2032735095","https://openalex.org/W2371749308","https://openalex.org/W2745905412","https://openalex.org/W1975803940"],"abstract_inverted_index":{"We":[0],"compute":[1],"the":[2,22,34,38,41],"number":[3],"of":[4,7,33,40],"rhombus":[5],"tilings":[6],"a":[8,44],"hexagon":[9,42],"with":[10],"sides":[11],"$n$,":[12,13,15,16],"$N$,":[14,17],"where":[18],"two":[19],"triangles":[20],"on":[21],"symmetry":[23],"axis":[24],"touching":[25],"in":[26],"one":[27],"vertex":[28,36],"are":[29],"removed.":[30],"The":[31],"case":[32],"common":[35],"being":[37],"center":[39],"solves":[43],"problem":[45],"posed":[46],"by":[47],"Propp.":[48]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}