{"id":"https://openalex.org/W2805361414","doi":"https://doi.org/10.37236/7412","title":"Symmetries of Shamrocks II: Axial Shamrocks","display_name":"Symmetries of Shamrocks II: Axial Shamrocks","publication_year":2018,"publication_date":"2018-06-08","ids":{"openalex":"https://openalex.org/W2805361414","doi":"https://doi.org/10.37236/7412","mag":"2805361414"},"language":"en","primary_location":{"id":"doi:10.37236/7412","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7412","pdf_url":null,"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://doi.org/10.37236/7412","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042226466","display_name":"Mihai Ciucu","orcid":"https://orcid.org/0000-0002-0942-5094"},"institutions":[{"id":"https://openalex.org/I592451","display_name":"Indiana University","ror":"https://ror.org/01kg8sb98","country_code":"US","type":"education","lineage":["https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mihai Ciucu","raw_affiliation_strings":["Indiana University"],"affiliations":[{"raw_affiliation_string":"Indiana University","institution_ids":["https://openalex.org/I592451"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5042226466"],"corresponding_institution_ids":["https://openalex.org/I592451"],"apc_list":null,"apc_paid":null,"fwci":0.099,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.38824694,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9909999966621399,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9872999787330627,"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":0.9480000138282776,"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/transpose","display_name":"Transpose","score":0.8314196467399597},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.7582169771194458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7530836462974548},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.673671305179596},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6624128818511963},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6499276161193848},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6038280129432678},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5460385084152222},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.523388683795929},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.42335954308509827},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3437041640281677},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2480696141719818},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16550230979919434},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08185160160064697},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.0780213475227356},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0646657645702362},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.05026346445083618}],"concepts":[{"id":"https://openalex.org/C200106649","wikidata":"https://www.wikidata.org/wiki/Q223683","display_name":"Transpose","level":3,"score":0.8314196467399597},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.7582169771194458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7530836462974548},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.673671305179596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6624128818511963},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6499276161193848},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6038280129432678},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5460385084152222},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.523388683795929},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.42335954308509827},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3437041640281677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2480696141719818},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16550230979919434},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08185160160064697},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0780213475227356},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0646657645702362},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.05026346445083618},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/7412","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7412","pdf_url":null,"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"},{"id":"pmh:oai:iu.tind.io:1483","is_oa":false,"landing_page_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i2p36","pdf_url":null,"source":{"id":"https://openalex.org/S4306402656","display_name":"IUScholarWorks Open (Indiana University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I592451","host_organization_name":"Indiana University","host_organization_lineage":["https://openalex.org/I592451"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://iu.tind.io/record/1483","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.37236/7412","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7412","pdf_url":null,"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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W2578985712","https://openalex.org/W2406961474","https://openalex.org/W2143566611","https://openalex.org/W588267724","https://openalex.org/W2057205169","https://openalex.org/W1566328901","https://openalex.org/W2392521623","https://openalex.org/W2770089535"],"abstract_inverted_index":{"The":[0,39,94],"first":[1],"paper":[2],"in":[3,44],"this":[4,31],"series":[5],"presented":[6],"the":[7,35,56,60,77,79,84,89],"enumeration":[8,95],"of":[9,20,55,59,96,98],"cyclically":[10,13],"symmetric,":[11],"and":[12,15,48],"symmetric":[14,57],"transpose":[16,36,80],"complementary":[17,37,81],"lozenge":[18],"tilings":[19],"a":[21,24],"hexagon":[22],"with":[23,64],"shamrock":[25],"removed":[26,66],"from":[27,67,101],"its":[28],"center.":[29],"In":[30],"article":[32],"we":[33,41,72],"address":[34],"case.":[38],"results":[40],"prove":[42],"are":[43],"fact":[45],"more":[46],"general":[47],"allow":[49],"us":[50],"to":[51,70],"give":[52],"an":[53],"extension":[54],"case":[58,82],"original":[61],"hexagonal":[62],"regions":[63],"shamrocks":[65],"their":[68],"center,":[69],"what":[71],"call":[73],"axial":[74],"shamrocks.":[75],"For":[76],"latter,":[78],"is":[83],"only":[85],"symmetry":[86],"class":[87],"besides":[88],"one":[90],"requiring":[91],"no":[92],"symmetries.":[93],"both":[97],"these":[99],"follows":[100],"our":[102],"results.":[103]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}