{"id":"https://openalex.org/W1965838677","doi":"https://doi.org/10.1142/s0218196711006121","title":"ON DIVIDED-DIFFERENCE SEMIGROUPS","display_name":"ON DIVIDED-DIFFERENCE SEMIGROUPS","publication_year":2011,"publication_date":"2011-02-01","ids":{"openalex":"https://openalex.org/W1965838677","doi":"https://doi.org/10.1142/s0218196711006121","mag":"1965838677"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196711006121","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196711006121","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://figshare.com/articles/journal_contribution/On_Divided-difference_semigroups/22881281","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111613905","display_name":"D. G. FitzGerald","orcid":null},"institutions":[{"id":"https://openalex.org/I129801699","display_name":"University of Tasmania","ror":"https://ror.org/01nfmeh72","country_code":"AU","type":"education","lineage":["https://openalex.org/I129801699"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"D. G. FITZGERALD","raw_affiliation_strings":["School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart 7001, Australia","School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, 7001, Australia"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart 7001, Australia","institution_ids":["https://openalex.org/I129801699"]},{"raw_affiliation_string":"School of Mathematics and Physics, University of Tasmania, Private Bag 37, Hobart, 7001, Australia","institution_ids":["https://openalex.org/I129801699"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111613905"],"corresponding_institution_ids":["https://openalex.org/I129801699"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07544836,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"21","issue":"01n02","first_page":"179","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9972000122070312,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9955000281333923,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9919999837875366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9353736639022827},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.9223663806915283},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.7011302709579468},{"id":"https://openalex.org/keywords/semigroup","display_name":"Semigroup","score":0.696082592010498},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.6006226539611816},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.5097746253013611},{"id":"https://openalex.org/keywords/point-group","display_name":"Point group","score":0.4504110813140869},{"id":"https://openalex.org/keywords/bicyclic-semigroup","display_name":"Bicyclic semigroup","score":0.4129263758659363},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3931679427623749},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34552377462387085}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9353736639022827},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.9223663806915283},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.7011302709579468},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.696082592010498},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.6006226539611816},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.5097746253013611},{"id":"https://openalex.org/C57796230","wikidata":"https://www.wikidata.org/wiki/Q899720","display_name":"Point group","level":2,"score":0.4504110813140869},{"id":"https://openalex.org/C40417594","wikidata":"https://www.wikidata.org/wiki/Q3022111","display_name":"Bicyclic semigroup","level":3,"score":0.4129263758659363},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3931679427623749},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34552377462387085},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s0218196711006121","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196711006121","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:eprints.utas.edu.au:9556","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922975","display_name":"UTAS Research 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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:ecite.utas.edu.au:68975","is_oa":false,"landing_page_url":"http://ecite.utas.edu.au/68975","pdf_url":null,"source":{"id":"https://openalex.org/S4306401569","display_name":"eCite Digital Repository (University of Tasmania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I129801699","host_organization_name":"University of Tasmania","host_organization_lineage":["https://openalex.org/I129801699"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Refereed Article"},{"id":"pmh:oai:figshare.com:article/22881281","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/On_Divided-difference_semigroups/22881281","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},{"id":"pmh:oai:figshare.com:article/23215571","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/On_divided-difference_semigroups/23215571","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/22881281","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/On_Divided-difference_semigroups/22881281","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"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":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2345852709","https://openalex.org/W2495029002"],"related_works":["https://openalex.org/W1569820777","https://openalex.org/W3088456608","https://openalex.org/W2527906400","https://openalex.org/W2362170751","https://openalex.org/W2015422204","https://openalex.org/W2991273408","https://openalex.org/W2952828667","https://openalex.org/W4301018163","https://openalex.org/W1970099719","https://openalex.org/W2898698596"],"abstract_inverted_index":{"The":[0],"Newtonian":[1],"divided-difference":[2],"operators":[3],"generate":[4],"the":[5,14,18,28,35,53],"nil-Coxeter":[6,15,54],"algebra":[7],"and":[8,17,30,58],"semigroup.":[9],"A":[10],"bijective":[11],"correspondence":[12],"between":[13],"semigroup":[16,55],"symmetric":[19],"group":[20,48],"is":[21],"used":[22],"to":[23,43],"provide":[24],"braid-like":[25],"diagrams":[26],"for":[27,34,40],"former,":[29],"corresponding":[31],"Reidemeister-type":[32],"moves":[33],"relations.":[36],"Conditions":[37],"are":[38,56],"given":[39,59],"similar":[41],"relations":[42],"hold":[44],"in":[45],"a":[46],"skew":[47],"ring.":[49],"Interesting":[50],"extensions":[51],"of":[52],"described":[57],"diagrammatic":[60],"representations.":[61]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}