{"id":"https://openalex.org/W3012070481","doi":"https://doi.org/10.37236/8716","title":"Lozenge Tilings of Hexagons with Central Holes and Dents","display_name":"Lozenge Tilings of Hexagons with Central Holes and Dents","publication_year":2020,"publication_date":"2020-03-19","ids":{"openalex":"https://openalex.org/W3012070481","doi":"https://doi.org/10.37236/8716","mag":"3012070481"},"language":"en","primary_location":{"id":"doi:10.37236/8716","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8716","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p61/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v27i1p61/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090266846","display_name":"Tri Lai","orcid":null},"institutions":[{"id":"https://openalex.org/I114395901","display_name":"University of Nebraska\u2013Lincoln","ror":"https://ror.org/043mer456","country_code":"US","type":"education","lineage":["https://openalex.org/I114395901"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tri Lai","raw_affiliation_strings":["University of Nebraska - Lincoln"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Nebraska - Lincoln","institution_ids":["https://openalex.org/I114395901"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090266846"],"corresponding_institution_ids":["https://openalex.org/I114395901"],"apc_list":null,"apc_paid":null,"fwci":3.8288,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.93719212,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"27","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9855999946594238,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9855999946594238,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9825000166893005,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11666","display_name":"Color Science and Applications","score":0.978600025177002,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7783553004264832},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7276610732078552},{"id":"https://openalex.org/keywords/equilateral-triangle","display_name":"Equilateral triangle","score":0.7239003777503967},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7217508554458618},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5580852031707764},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5418731570243835},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.533137321472168},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4378732740879059},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.42636778950691223},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23837092518806458},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09743425250053406}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7783553004264832},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7276610732078552},{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.7239003777503967},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7217508554458618},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5580852031707764},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5418731570243835},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.533137321472168},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4378732740879059},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.42636778950691223},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23837092518806458},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09743425250053406},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/8716","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8716","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p61/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/8716","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8716","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p61/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3012070481.pdf","grobid_xml":"https://content.openalex.org/works/W3012070481.grobid-xml"},"referenced_works_count":56,"referenced_works":["https://openalex.org/W1486693003","https://openalex.org/W1495330071","https://openalex.org/W1568032701","https://openalex.org/W1580474764","https://openalex.org/W1613412028","https://openalex.org/W1614039283","https://openalex.org/W1715153673","https://openalex.org/W1751653348","https://openalex.org/W1788197430","https://openalex.org/W1802750051","https://openalex.org/W1844146324","https://openalex.org/W1965182961","https://openalex.org/W1974219541","https://openalex.org/W1977628371","https://openalex.org/W1978581879","https://openalex.org/W1991885341","https://openalex.org/W1992294562","https://openalex.org/W2038782505","https://openalex.org/W2064675360","https://openalex.org/W2069754269","https://openalex.org/W2075664384","https://openalex.org/W2077004953","https://openalex.org/W2078635841","https://openalex.org/W2105759001","https://openalex.org/W2113542586","https://openalex.org/W2119072491","https://openalex.org/W2125478358","https://openalex.org/W2133024463","https://openalex.org/W2135025148","https://openalex.org/W2168654091","https://openalex.org/W2257093477","https://openalex.org/W2276826925","https://openalex.org/W2299166221","https://openalex.org/W2591904460","https://openalex.org/W2776184378","https://openalex.org/W2781970145","https://openalex.org/W2946604395","https://openalex.org/W2948155886","https://openalex.org/W2949089804","https://openalex.org/W2952336157","https://openalex.org/W2952478927","https://openalex.org/W2962986186","https://openalex.org/W2963140391","https://openalex.org/W2963482895","https://openalex.org/W2963559095","https://openalex.org/W2963872559","https://openalex.org/W2964043481","https://openalex.org/W2964279235","https://openalex.org/W2992272554","https://openalex.org/W3000558403","https://openalex.org/W3037479919","https://openalex.org/W3140733793","https://openalex.org/W4248937387","https://openalex.org/W4312069279","https://openalex.org/W6669565411","https://openalex.org/W6679926264"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W3204326392","https://openalex.org/W2508087100","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W3161792707","https://openalex.org/W2500000936","https://openalex.org/W2086778274","https://openalex.org/W2780411548"],"abstract_inverted_index":{"Ciucu":[0],"proved":[1],"a":[2,11,15,24,40,53,82],"simple":[3],"product":[4],"formula":[5,88],"for":[6,52],"the":[7,30,60,76,95,98],"tiling":[8,50],"number":[9],"of":[10,17,20,43,75,85,89,97,100],"hexagon":[12,54],"in":[13,64],"which":[14],"chain":[16],"equilateral":[18],"triangles":[19],"alternating":[21],"orientations,":[22],"called":[23],"`fern',":[25],"has":[26],"been":[27],"removed":[28],"from":[29,72],"center":[31],"(Adv.":[32],"Math.":[33],"2017).":[34],"In":[35],"this":[36,44],"paper,":[37],"we":[38,67],"present":[39],"multi-parameter":[41],"generalization":[42],"work":[45],"by":[46,106],"giving":[47],"an":[48],"explicit":[49],"enumeration":[51],"with":[55],"three":[56,101],"ferns":[57,71],"removed,":[58],"besides":[59],"central":[61],"fern":[62],"as":[63],"Ciucu's":[65],"region,":[66],"remove":[68],"two":[69,73],"new":[70,83],"sides":[74],"hexagon.":[77],"Our":[78],"result":[79],"also":[80],"implies":[81],"`dual'":[84],"MacMahon's":[86],"classical":[87],"boxed":[90],"plane":[91],"partitions,":[92],"corresponding":[93],"to":[94],"exterior":[96],"union":[99],"disjoint":[102],"concave":[103],"polygons":[104],"obtained":[105],"turning":[107],"120":[108],"degrees":[109],"after":[110],"drawing":[111],"each":[112],"side.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}