{"id":"https://openalex.org/W4410243886","doi":"https://doi.org/10.1142/s0218196725500183","title":"Pretzel Monoids","display_name":"Pretzel Monoids","publication_year":2025,"publication_date":"2025-05-09","ids":{"openalex":"https://openalex.org/W4410243886","doi":"https://doi.org/10.1142/s0218196725500183"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196725500183","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500183","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":true,"oa_status":"green","oa_url":"https://research.manchester.ac.uk/files/1508524242/Pretzel_Monoids_Mar25.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Daniel Heath","orcid":"https://orcid.org/0000-0001-5811-4949"},"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":"Daniel Heath","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Manchester M13 9PL, UK"],"raw_orcid":"https://orcid.org/0000-0001-5811-4949","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041232556","display_name":"Mark Kambites","orcid":null},"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":false,"raw_author_name":"Mark Kambites","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Manchester M13 9PL, UK"],"raw_orcid":"https://orcid.org/0000-0002-0656-8014","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Manchester M13 9PL, UK","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034824480","display_name":"N\u00f3ra Szak\u00e1cs","orcid":"https://orcid.org/0000-0002-4098-1988"},"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":false,"raw_author_name":"N\u00f3ra Szak\u00e1cs","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Manchester M13 9PL, UK"],"raw_orcid":"https://orcid.org/0000-0002-4098-1988","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":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I28407311"],"apc_list":null,"apc_paid":null,"fwci":1.1902,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.80551591,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"35","issue":"05","first_page":"647","last_page":"685"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9473000168800354,"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/T11567","display_name":"semigroups and automata theory","score":0.9473000168800354,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9251564741134644},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5124552845954895},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.392566055059433},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34895059466362}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9251564741134644},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5124552845954895},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.392566055059433},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34895059466362}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s0218196725500183","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196725500183","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:publications/c29f604a-8124-4c0b-b412-c6fcd6cb2bca","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/c29f604a-8124-4c0b-b412-c6fcd6cb2bca","pdf_url":"https://research.manchester.ac.uk/files/1508524242/Pretzel_Monoids_Mar25.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Heath, D, Kambites, M & Szak\u00e1cs, N 2025, 'Pretzel Monoids', International Journal of Algebra and Computation, vol. 35, no. 05, pp. 647-685. https://doi.org/10.1142/S0218196725500183","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:publications/c29f604a-8124-4c0b-b412-c6fcd6cb2bca","is_oa":true,"landing_page_url":"https://research.manchester.ac.uk/en/publications/c29f604a-8124-4c0b-b412-c6fcd6cb2bca","pdf_url":"https://research.manchester.ac.uk/files/1508524242/Pretzel_Monoids_Mar25.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Heath, D, Kambites, M & Szak\u00e1cs, N 2025, 'Pretzel Monoids', International Journal of Algebra and Computation, vol. 35, no. 05, pp. 647-685. https://doi.org/10.1142/S0218196725500183","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410243886.pdf","grobid_xml":"https://content.openalex.org/works/W4410243886.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1487875360","https://openalex.org/W1978237159","https://openalex.org/W2019682114","https://openalex.org/W2024194200","https://openalex.org/W2029884820","https://openalex.org/W2052423274","https://openalex.org/W2067309274","https://openalex.org/W2070740841","https://openalex.org/W2073279331","https://openalex.org/W2074599978","https://openalex.org/W2079300096","https://openalex.org/W2082682599","https://openalex.org/W2084172755","https://openalex.org/W2084543966","https://openalex.org/W2101716083","https://openalex.org/W2102915915","https://openalex.org/W2137694135","https://openalex.org/W2152183767","https://openalex.org/W2153126460","https://openalex.org/W2153632678","https://openalex.org/W2160584888","https://openalex.org/W2327582114","https://openalex.org/W2884489849","https://openalex.org/W2964351516","https://openalex.org/W4205567970","https://openalex.org/W4212828952","https://openalex.org/W4293176479"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0],"introduce":[1],"an":[2],"interesting":[3],"class":[4,51],"of":[5,21,44,52,64,77,91],"left":[6,45,74,93],"adequate":[7,46,75,94],"monoids":[8,20,47,95],"which":[9],"we":[10],"call":[11],"pretzel":[12],"monoids.":[13,82],"These,":[14],"on":[15,32],"the":[16,33,42,60,73,86,97],"one":[17],"hand,":[18,35],"are":[19,36,55],"birooted":[22],"graphs":[23],"with":[24],"respect":[25],"to":[26,38,58],"a":[27,49],"natural":[28,50],"\u2018glue-and-fold\u2019":[29],"operation,":[30],"and":[31],"other":[34],"shown":[37,57],"be":[39,59],"defined":[40],"in":[41,70],"category":[43],"by":[48],"presentations.":[53],"They":[54],"also":[56],"free":[61,92],"idempotent-pure":[62],"expansions":[63,79],"right":[65,98],"cancellative":[66,99],"monoids,":[67],"making":[68],"them,":[69],"some":[71],"sense,":[72],"analogues":[76],"Margolis\u2013Meakin":[78],"for":[80],"inverse":[81],"The":[83],"construction":[84],"recovers":[85],"second":[87],"author\u2019s":[88],"geometric":[89],"model":[90],"when":[96],"monoid":[100],"is":[101],"free.":[102]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-05-10T00:00:00"}