{"id":"https://openalex.org/W7162142806","doi":"https://doi.org/10.1016/j.tcs.2026.116024","title":"Bernoulli sets over ternary and multiletter alphabets: Algebraic characterizations, polynomial divisibility, and commutative prefix properties","display_name":"Bernoulli sets over ternary and multiletter alphabets: Algebraic characterizations, polynomial divisibility, and commutative prefix properties","publication_year":2026,"publication_date":"2026-05-22","ids":{"openalex":"https://openalex.org/W7162142806","doi":"https://doi.org/10.1016/j.tcs.2026.116024"},"language":"en","primary_location":{"id":"doi:10.1016/j.tcs.2026.116024","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.tcs.2026.116024","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","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/A5136737544","display_name":"Haiyan Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I49185572","display_name":"Yunnan University of Finance And Economics","ror":"https://ror.org/04rhev598","country_code":"CN","type":"education","lineage":["https://openalex.org/I49185572"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haiyan Liu","raw_affiliation_strings":["School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, PR China","institution_ids":["https://openalex.org/I49185572"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111093709","display_name":"Rongdong Cui","orcid":null},"institutions":[{"id":"https://openalex.org/I61565387","display_name":"Dalian Minzu University","ror":"https://ror.org/02hxfx521","country_code":"CN","type":"education","lineage":["https://openalex.org/I61565387"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rongdong Cui","raw_affiliation_strings":["The Nationalities High School of Dali Bai Autonomous Prefecture, Dali, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Nationalities High School of Dali Bai Autonomous Prefecture, Dali, PR China","institution_ids":["https://openalex.org/I61565387"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101423950","display_name":"Tianjie Zhang","orcid":"https://orcid.org/0000-0003-3810-2582"},"institutions":[{"id":"https://openalex.org/I21642278","display_name":"Ningxia University","ror":"https://ror.org/04j7b2v61","country_code":"CN","type":"education","lineage":["https://openalex.org/I21642278"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tianjie Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Ningxia University, Yinchuan, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Ningxia University, Yinchuan, PR China","institution_ids":["https://openalex.org/I21642278"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5136806606","display_name":"Shuo Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I49185572","display_name":"Yunnan University of Finance And Economics","ror":"https://ror.org/04rhev598","country_code":"CN","type":"education","lineage":["https://openalex.org/I49185572"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuo Zhang","raw_affiliation_strings":["School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, PR China","institution_ids":["https://openalex.org/I49185572"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5136737544"],"corresponding_institution_ids":["https://openalex.org/I49185572"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.63381093,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"1080","issue":null,"first_page":"116024","last_page":"116024"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.7368000149726868,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11130","display_name":"Coding theory and cryptography","score":0.7368000149726868,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11567","display_name":"semigroups and automata theory","score":0.06960000097751617,"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/T10142","display_name":"Formal Methods in Verification","score":0.025100000202655792,"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/semiring","display_name":"Semiring","score":0.5755000114440918},{"id":"https://openalex.org/keywords/bernoullis-principle","display_name":"Bernoulli's principle","score":0.546500027179718},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.45500001311302185},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.4406000077724457},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.42750000953674316},{"id":"https://openalex.org/keywords/algebraic-theory","display_name":"Algebraic theory","score":0.41920000314712524},{"id":"https://openalex.org/keywords/prefix","display_name":"Prefix","score":0.41670000553131104},{"id":"https://openalex.org/keywords/algebraic-structure","display_name":"Algebraic structure","score":0.3797000050544739},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.3743000030517578}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6843000054359436},{"id":"https://openalex.org/C21696900","wikidata":"https://www.wikidata.org/wiki/Q1333055","display_name":"Semiring","level":2,"score":0.5755000114440918},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5683000087738037},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.546500027179718},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.45500001311302185},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.42750000953674316},{"id":"https://openalex.org/C2779782106","wikidata":"https://www.wikidata.org/wiki/Q4724020","display_name":"Algebraic theory","level":3,"score":0.41920000314712524},{"id":"https://openalex.org/C141603448","wikidata":"https://www.wikidata.org/wiki/Q134830","display_name":"Prefix","level":2,"score":0.41670000553131104},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3822000026702881},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.3797000050544739},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C20079647","wikidata":"https://www.wikidata.org/wiki/Q1278039","display_name":"Prefix code","level":5,"score":0.37299999594688416},{"id":"https://openalex.org/C2989065042","wikidata":"https://www.wikidata.org/wiki/Q7378971","display_name":"Algebraic properties","level":2,"score":0.36719998717308044},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.3610999882221222},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3278999924659729},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.31630000472068787},{"id":"https://openalex.org/C164528419","wikidata":"https://www.wikidata.org/wiki/Q3042439","display_name":"Bernoulli scheme","level":3,"score":0.3109999895095825},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.2888000011444092},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.27959999442100525},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C137212723","wikidata":"https://www.wikidata.org/wiki/Q1948412","display_name":"Morphism","level":2,"score":0.2558000087738037}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.tcs.2026.116024","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.tcs.2026.116024","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.7171564698219299,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1991162149","https://openalex.org/W1997747484","https://openalex.org/W2028607284","https://openalex.org/W2048554767","https://openalex.org/W2059571075","https://openalex.org/W2060628618","https://openalex.org/W2070912355","https://openalex.org/W2124314201","https://openalex.org/W2552028135","https://openalex.org/W3120475523"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-05-28T06:12:49.907903","created_date":"2026-05-23T00:00:00"}
