{"id":"https://openalex.org/W7220971476","doi":"https://doi.org/10.48550/arxiv.2610.07999","title":"On the number of cokernel-closed additive subcategories for uniformly oriented $A_n$ quivers","display_name":"On the number of cokernel-closed additive subcategories for uniformly oriented $A_n$ quivers","publication_year":2026,"publication_date":"2026-10-06","ids":{"openalex":"https://openalex.org/W7220971476","doi":"https://doi.org/10.48550/arxiv.2610.07999"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.07999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07999","pdf_url":"https://arxiv.org/pdf/2610.07999","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.07999","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007688099","display_name":"Volodymyr Mazorchuk","orcid":"https://orcid.org/0000-0002-4633-6218","observed_orcids":["https://orcid.org/0000-0002-4633-6218"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mazorchuk, Volodymyr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5022676221","display_name":"Shuoyang Xu","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xu, Shuoyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.6650000214576721,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.6650000214576721,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.32710000872612,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.000699999975040555,"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/full-subcategories","display_name":"full subcategories","score":0.671999990940094},{"id":"https://openalex.org/keywords/catalan-numbers","display_name":"Catalan numbers","score":0.652999997138977},{"id":"https://openalex.org/keywords/integer-sequences","display_name":"integer sequences","score":0.7710000276565552},{"id":"https://openalex.org/keywords/meet-irreducible-elements","display_name":"meet-irreducible elements","score":0.9950000047683716}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.769599974155426},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6773999929428101},{"id":"https://openalex.org/C172252984","wikidata":"https://www.wikidata.org/wiki/Q368988","display_name":"Idempotence","level":2,"score":0.6337000131607056},{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.5077999830245972},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.48420000076293945},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.478300005197525},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4560999870300293},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38420000672340393},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.3749000132083893},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3691999912261963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36820000410079956},{"id":"https://openalex.org/C61994974","wikidata":"https://www.wikidata.org/wiki/Q2297602","display_name":"Integer sequence","level":3,"score":0.3677000105381012},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.2793999910354614},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.07999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07999","pdf_url":"https://arxiv.org/pdf/2610.07999","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.07999","doi":"https://doi.org/10.48550/arxiv.2610.07999","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.07999","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.07999","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.07999","pdf_url":"https://arxiv.org/pdf/2610.07999","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220971476.pdf","grobid_xml":"https://content.openalex.org/works/W7220971476.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7127120469","https://openalex.org/W7167100715","https://openalex.org/W7203754159"],"related_works":["https://openalex.org/W3102743765","https://openalex.org/W2341575154","https://openalex.org/W7064643119","https://openalex.org/W2749401033","https://openalex.org/W6885102163","https://openalex.org/W2901402641","https://openalex.org/W1973666875","https://openalex.org/W2999680697","https://openalex.org/W175625198","https://openalex.org/W6923552610"],"abstract_inverted_index":{"We":[0,47],"study":[1],"the":[2,14,54,57,67],"integer":[3],"sequence":[4,38],"that":[5,72],"enumerates":[6],"cokernel-closed,":[7],"idempotent":[8],"split,":[9],"full,":[10],"additive":[11],"subcategories":[12],"of":[13,16,21,36,53,66,71],"category":[15],"finite":[17],"dimensional":[18],"complex":[19],"representations":[20],"a":[22,28,33],"uniformly":[23],"oriented":[24],"$A_n$":[25],"quiver.":[26],"Using":[27],"combinatorial":[29],"model,":[30],"we":[31,61],"describe":[32,49],"non-obvious":[34],"connection":[35],"this":[37],"to":[39],"Catalan":[40],"numbers":[41],"and":[42],"derive":[43],"an":[44,63],"implicit":[45],"recurrence.":[46],"also":[48],"some":[50],"basic":[51],"properties":[52],"lattice":[55],"underlying":[56],"sequences,":[58],"in":[59],"particular,":[60],"give":[62],"explicit":[64],"description":[65],"meet":[68],"irreducible":[69],"elements":[70],"lattice.":[73]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
