{"id":"https://openalex.org/W2890257444","doi":"https://doi.org/10.1080/10586458.2019.1577768","title":"Quotients of the Magmatic Operad: Lattice Structures and Convergent Rewrite Systems","display_name":"Quotients of the Magmatic Operad: Lattice Structures and Convergent Rewrite Systems","publication_year":2019,"publication_date":"2019-03-31","ids":{"openalex":"https://openalex.org/W2890257444","doi":"https://doi.org/10.1080/10586458.2019.1577768","mag":"2890257444"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2019.1577768","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2019.1577768","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1809.05083","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016694492","display_name":"Cyrille Chenavier","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I2800365227","display_name":"Paris-Est Sup","ror":"https://ror.org/0268ecp52","country_code":"FR","type":"education","lineage":["https://openalex.org/I2800365227"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cyrille Chenavier","raw_affiliation_strings":["Universit\u00e9 Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, Marne-la-Vall\u00c9e, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, Marne-la-Vall\u00c9e, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I2800365227","https://openalex.org/I1294671590","https://openalex.org/I4210154111"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085751823","display_name":"Christophe Cordero","orcid":null},"institutions":[{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I2800365227","display_name":"Paris-Est Sup","ror":"https://ror.org/0268ecp52","country_code":"FR","type":"education","lineage":["https://openalex.org/I2800365227"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Christophe Cordero","raw_affiliation_strings":["Universit\u00e9 Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, Marne-la-Vall\u00c9e, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, Marne-la-Vall\u00c9e, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I2800365227","https://openalex.org/I1294671590","https://openalex.org/I4210154111"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035678818","display_name":"Samuele Giraudo","orcid":"https://orcid.org/0000-0003-3878-371X"},"institutions":[{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I2800365227","display_name":"Paris-Est Sup","ror":"https://ror.org/0268ecp52","country_code":"FR","type":"education","lineage":["https://openalex.org/I2800365227"]},{"id":"https://openalex.org/I4210152518","display_name":"Laboratoire d'Informatique Gaspard-Monge","ror":"https://ror.org/04t50yk91","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210145102","https://openalex.org/I4210152518","https://openalex.org/I4210154111","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Samuele Giraudo","raw_affiliation_strings":["Universit\u00e9 Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, Marne-la-Vall\u00c9e, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Paris-Est, LIGM (UMR 8049), CNRS, ENPC, ESIEE Paris, UPEM, Marne-la-Vall\u00c9e, France","institution_ids":["https://openalex.org/I4210152518","https://openalex.org/I2800365227","https://openalex.org/I1294671590","https://openalex.org/I4210154111"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035678818"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2800365227","https://openalex.org/I4210152518","https://openalex.org/I4210154111"],"apc_list":null,"apc_paid":null,"fwci":0.9501,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69121339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"30","issue":"4","first_page":"513","last_page":"530"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11673","display_name":"Advanced Topics in Algebra","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9994999766349792,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8333268761634827},{"id":"https://openalex.org/keywords/associative-property","display_name":"Associative property","score":0.7055047154426575},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.7044479250907898},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6972342133522034},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5048094987869263},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.4370793104171753},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3253335952758789},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06416782736778259}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8333268761634827},{"id":"https://openalex.org/C159423971","wikidata":"https://www.wikidata.org/wiki/Q177251","display_name":"Associative property","level":2,"score":0.7055047154426575},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.7044479250907898},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6972342133522034},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5048094987869263},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.4370793104171753},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3253335952758789},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06416782736778259},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2019.1577768","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2019.1577768","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1809.05083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.05083","pdf_url":"https://arxiv.org/pdf/1809.05083","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-03152576v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03152576","pdf_url":"https://hal.science/hal-03152576v1/document","source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Experimental Mathematics, 2019, ⟨10.1080/10586458.2019.1577768⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1809.05083","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1809.05083","pdf_url":"https://arxiv.org/pdf/1809.05083","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W172574161","https://openalex.org/W1583295953","https://openalex.org/W1972757708","https://openalex.org/W1978343152","https://openalex.org/W2013071320","https://openalex.org/W2021827119","https://openalex.org/W2050003317","https://openalex.org/W2051725919","https://openalex.org/W2123466867","https://openalex.org/W2129142192","https://openalex.org/W2163792765","https://openalex.org/W2323378191","https://openalex.org/W2803758272","https://openalex.org/W2920477253","https://openalex.org/W2963366983","https://openalex.org/W2963599377","https://openalex.org/W3100315854","https://openalex.org/W3100542400","https://openalex.org/W3102094360","https://openalex.org/W3198160809","https://openalex.org/W4213382433","https://openalex.org/W4230919050","https://openalex.org/W4252614677"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2949502838","https://openalex.org/W2070443794","https://openalex.org/W4313895414","https://openalex.org/W2928193004","https://openalex.org/W1492794944","https://openalex.org/W2914488349","https://openalex.org/W3041175538","https://openalex.org/W1994030850","https://openalex.org/W260863705"],"abstract_inverted_index":{"We":[0,68],"study":[1,114],"quotients":[2,28,115],"of":[3,26,38,45,73,85,116],"the":[4,9,18,24,39,43,49,65,71,83,90,104,117],"magmatic":[5,118],"operad":[6,12,107,119],"that":[7,23,57,70],"is":[8],"free":[10],"nonsymmetric":[11],"over":[13],"one":[14,121],"binary":[15],"generator.":[16],"In":[17,48],"linear":[19],"setting,":[20,51],"we":[21,34,52,97,113],"show":[22,35,69],"set":[25,72],"these":[27,46],"admits":[29,77],"a":[30,78,99],"lattice":[31,79,84],"structure":[32],"and":[33,129],"an":[36],"analog":[37],"Grassmann":[40],"formula":[41],"for":[42,103],"dimensions":[44],"operads.":[47],"nonlinear":[50],"define":[53],"comb":[54,74,105],"associative":[55,66,75,106],"operads":[56,59,76],"are":[58],"indexed":[60],"by":[61,94,120,124],"non-negative":[62,86],"integers":[63,87],"generalizing":[64],"operad.":[67],"structure,":[80],"isomorphic":[81],"to":[82],"equipped":[88],"with":[89,110],"division":[91],"order.":[92],"Driven":[93],"computer":[95],"experimentations,":[96],"provide":[98],"finite":[100],"convergent":[101],"presentation":[102],"in":[108],"correspondence":[109],"3.":[111],"Finally,":[112],"cubic":[122],"relation":[123],"expressing":[125],"their":[126],"Hilbert":[127],"series":[128],"providing":[130],"combinatorial":[131],"realizations.":[132]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2018-09-27T00:00:00"}