{"id":"https://openalex.org/W2995588377","doi":"https://doi.org/10.1007/s10208-023-09609-8","title":"Symmetry and Invariant Bases in Finite Element Exterior Calculus","display_name":"Symmetry and Invariant Bases in Finite Element Exterior Calculus","publication_year":2023,"publication_date":"2023-04-27","ids":{"openalex":"https://openalex.org/W2995588377","doi":"https://doi.org/10.1007/s10208-023-09609-8","mag":"2995588377"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-023-09609-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10208-023-09609-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09609-8.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09609-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054231430","display_name":"Martin W. Licht","orcid":"https://orcid.org/0000-0002-7675-2255"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Martin W. Licht","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015, Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne (EPFL), 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5054231430"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.1214,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.27048923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"24","issue":"4","first_page":"1185","last_page":"1224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9933000206947327,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9797999858856201,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8816288709640503},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.6084498167037964},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.5965825915336609},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4966915249824524},{"id":"https://openalex.org/keywords/finite-group","display_name":"Finite group","score":0.4795648455619812},{"id":"https://openalex.org/keywords/invariant-theory","display_name":"Invariant theory","score":0.41335758566856384},{"id":"https://openalex.org/keywords/representation-theory","display_name":"Representation theory","score":0.28137439489364624},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.26328498125076294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13717952370643616}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8816288709640503},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6084498167037964},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5965825915336609},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4966915249824524},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.4795648455619812},{"id":"https://openalex.org/C63036529","wikidata":"https://www.wikidata.org/wiki/Q1855669","display_name":"Invariant theory","level":3,"score":0.41335758566856384},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.28137439489364624},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.26328498125076294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13717952370643616},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-023-09609-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10208-023-09609-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09609-8.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:302513","is_oa":true,"landing_page_url":"https://infoscience.epfl.ch/handle/20.500.14299/197711","pdf_url":"https://infoscience.epfl.ch/bitstreams/b51896eb-c1dc-424a-9225-75289672dc85/download","source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"research article"}],"best_oa_location":{"id":"doi:10.1007/s10208-023-09609-8","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s10208-023-09609-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09609-8.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3728093668","display_name":"Isaac Newton Institute for Mathematical Sciences","funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G3749500070","display_name":"RTG: An Interdisciplinary Research Training Program in Applied Mathematics, Computational Science, and Mathematical Physics","funder_award_id":"1345013","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4421442999","display_name":null,"funder_award_id":"EP/K032208","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4947591155","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5128091834","display_name":null,"funder_award_id":"EP/K032208/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5452750012","display_name":"Structure and scaling in computational field theories","funder_award_id":"278011","funder_id":"https://openalex.org/F4320338352","funder_display_name":"FP7 Ideas: European Research Council"},{"id":"https://openalex.org/G6068406125","display_name":"FRG: Collaborative Research: Analysis of the Einstein Constraint Equations","funder_award_id":"1262982","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6205422910","display_name":null,"funder_award_id":"1345013","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"},{"id":"https://openalex.org/F4320338352","display_name":"FP7 Ideas: European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2995588377.pdf","grobid_xml":"https://content.openalex.org/works/W2995588377.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W136185420","https://openalex.org/W259418976","https://openalex.org/W1500894486","https://openalex.org/W1534413569","https://openalex.org/W1579486099","https://openalex.org/W1779617503","https://openalex.org/W1967249709","https://openalex.org/W1975977317","https://openalex.org/W1987628609","https://openalex.org/W1992923859","https://openalex.org/W1994388915","https://openalex.org/W2001890369","https://openalex.org/W2009940960","https://openalex.org/W2017928198","https://openalex.org/W2017976561","https://openalex.org/W2022368757","https://openalex.org/W2025592734","https://openalex.org/W2034024171","https://openalex.org/W2039660064","https://openalex.org/W2051682834","https://openalex.org/W2051799546","https://openalex.org/W2056357222","https://openalex.org/W2064909895","https://openalex.org/W2084038014","https://openalex.org/W2089344418","https://openalex.org/W2121168715","https://openalex.org/W2131341034","https://openalex.org/W2135528252","https://openalex.org/W2135723931","https://openalex.org/W2137031984","https://openalex.org/W2138486270","https://openalex.org/W2143783905","https://openalex.org/W2145602099","https://openalex.org/W2157125378","https://openalex.org/W2157325488","https://openalex.org/W2169266183","https://openalex.org/W2581985288","https://openalex.org/W2583640341","https://openalex.org/W2587893739","https://openalex.org/W2594348025","https://openalex.org/W2746980166","https://openalex.org/W2895457232","https://openalex.org/W2903954990","https://openalex.org/W2906022956","https://openalex.org/W2909878113","https://openalex.org/W2950003260","https://openalex.org/W2964032145","https://openalex.org/W2964101930","https://openalex.org/W2970789867","https://openalex.org/W3099687355","https://openalex.org/W3103476862","https://openalex.org/W4242918424","https://openalex.org/W4297936497","https://openalex.org/W6601780613"],"related_works":["https://openalex.org/W2088544526","https://openalex.org/W2969166246","https://openalex.org/W4230583768","https://openalex.org/W1978679034","https://openalex.org/W4200342077","https://openalex.org/W163171588","https://openalex.org/W2159651761","https://openalex.org/W4382173277","https://openalex.org/W2963092292","https://openalex.org/W4297699348"],"abstract_inverted_index":{"Abstract":[0],"We":[1,17,61,83,91],"study":[2],"symmetries":[3,108],"of":[4,31,36,44,66,80,97,101,109,116,137],"bases":[5,27,123],"and":[6,68,74,94,105,113,132],"spanning":[7],"sets":[8],"in":[9,129],"finite":[10,23,54,118,138],"element":[11,24,55,119,139],"exterior":[12],"calculus,":[13],"using":[14],"representation":[15],"theory.":[16],"want":[18],"to":[19,40],"know":[20],"which":[21],"vector-valued":[22],"spaces":[25,56,136],"have":[26],"invariant":[28,81,122],"under":[29],"permutation":[30],"vertex":[32,37],"indices.":[33],"The":[34],"permutations":[35],"indices":[38],"correspond":[39],"the":[41,45,58,72,78,102,110,117],"symmetry":[42,48],"group":[43,49,104],"simplex.":[46],"That":[47],"is":[50],"represented":[51],"on":[52,71],"simplicial":[53],"by":[57],"pullback":[59],"action.":[60],"determine":[62],"a":[63],"natural":[64],"notion":[65],"invariance":[67],"sufficient":[69],"conditions":[70,87],"dimension":[73],"polynomial":[75],"degree":[76],"for":[77,134],"existence":[79],"bases.":[82],"conjecture":[84],"that":[85],"these":[86],"are":[88,127],"necessary":[89],"too.":[90],"utilize":[92],"Djokovi\u0107":[93],"Malzan\u2019s":[95],"classification":[96],"monomial":[98],"irreducible":[99],"representations":[100],"symmetric":[103],"show":[106],"new":[107],"geometric":[111],"decomposition":[112],"canonical":[114],"isomorphisms":[115],"spaces.":[120],"Explicit":[121],"with":[124],"complex":[125],"coefficients":[126],"constructed":[128],"dimensions":[130],"two":[131],"three":[133],"different":[135],"differential":[140],"forms.":[141]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2025-10-10T00:00:00"}
