{"id":"https://openalex.org/W4293249936","doi":"https://doi.org/10.1142/s0218196722500461","title":"Identities of tropical matrix semigroups and the plactic monoid of rank 4","display_name":"Identities of tropical matrix semigroups and the plactic monoid of rank 4","publication_year":2022,"publication_date":"2022-04-28","ids":{"openalex":"https://openalex.org/W4293249936","doi":"https://doi.org/10.1142/s0218196722500461"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196722500461","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196722500461","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090926062","display_name":"Thomas Aird","orcid":"https://orcid.org/0000-0002-9274-9822"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Thomas Aird","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Manchester M13 9PL, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090926062"],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":0.1461,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48547499,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"06","first_page":"1083","last_page":"1100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.996999979019165,"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"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.996999979019165,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9837999939918518,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9704999923706055,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.8963292837142944},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.864190936088562},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.7275304794311523},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.666861891746521},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.6585127115249634},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6246008276939392},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5504572987556458},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5256824493408203},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.42913731932640076},{"id":"https://openalex.org/keywords/cancellative-semigroup","display_name":"Cancellative semigroup","score":0.41715970635414124},{"id":"https://openalex.org/keywords/triangular-matrix","display_name":"Triangular matrix","score":0.4106171131134033},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40039902925491333},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3283580243587494},{"id":"https://openalex.org/keywords/invertible-matrix","display_name":"Invertible matrix","score":0.052002936601638794}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8963292837142944},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.864190936088562},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.7275304794311523},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.666861891746521},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.6585127115249634},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6246008276939392},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5504572987556458},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5256824493408203},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.42913731932640076},{"id":"https://openalex.org/C21112865","wikidata":"https://www.wikidata.org/wiki/Q5031372","display_name":"Cancellative semigroup","level":3,"score":0.41715970635414124},{"id":"https://openalex.org/C104528550","wikidata":"https://www.wikidata.org/wiki/Q506265","display_name":"Triangular matrix","level":3,"score":0.4106171131134033},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40039902925491333},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3283580243587494},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.052002936601638794},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196722500461","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196722500461","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/975ccb52-b061-492b-a25b-7a4e5fcd3d68","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/975ccb52-b061-492b-a25b-7a4e5fcd3d68","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Aird, T 2022, 'Identities of tropical matrix semigroups and the plactic monoid of rank 4', International Journal of Algebra and Computation, vol. 32, no. 6, 10.1142/S0218196722500461, pp. 1083 - 1100. https://doi.org/10.1142/S0218196722500461","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1495088152","https://openalex.org/W1539744609","https://openalex.org/W1582044446","https://openalex.org/W1976534037","https://openalex.org/W2017875602","https://openalex.org/W2033701980","https://openalex.org/W2083844723","https://openalex.org/W2168316830","https://openalex.org/W2286227792","https://openalex.org/W2341887449","https://openalex.org/W2794269212","https://openalex.org/W3125551652","https://openalex.org/W3204050946","https://openalex.org/W4235936977","https://openalex.org/W4237506113","https://openalex.org/W4242599214"],"related_works":["https://openalex.org/W4212828952","https://openalex.org/W2465992524","https://openalex.org/W2085193533","https://openalex.org/W2361990078","https://openalex.org/W3149550234","https://openalex.org/W2360953830","https://openalex.org/W4367000290","https://openalex.org/W2014389955","https://openalex.org/W2983428786","https://openalex.org/W4293249936"],"abstract_inverted_index":{"We":[0,20,43],"study":[1],"semigroup":[2,28,35,66,99],"varieties":[3],"generated":[4,101,112],"by":[5,86,102,113],"full":[6,53,56],"and":[7,13,95],"upper":[8,24],"triangular":[9,25],"tropical":[10,26,57],"matrix":[11,27,54,58],"semigroups":[12,59],"the":[14,23,52,69,98,110],"plactic":[15,70],"monoid":[16,71],"of":[17,48,60,72,83],"rank":[18,73],"4.":[19],"prove":[21],"that":[22,97],"[Formula:":[29,40,75,87,103,114],"see":[30,41,76,88,104,115],"text]":[31,89,105],"generates":[32],"a":[33,45,80],"different":[34,61,65],"variety":[36,100,111],"for":[37,51],"each":[38],"dimension":[39],"text].":[42,116],"show":[44,96],"weaker":[46],"version":[47],"this":[49],"fact":[50],"semigroup:":[55],"prime":[62],"dimensions":[63],"generate":[64],"varieties.":[67],"For":[68],"4,":[74],"text],":[77],"we":[78],"find":[79],"new":[81],"set":[82],"identities":[84],"satisfied":[85],"shorter":[90],"than":[91],"those":[92],"previously":[93],"known,":[94],"is":[106],"strictly":[107],"contained":[108],"in":[109]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
