{"id":"https://openalex.org/W7214907817","doi":"https://doi.org/10.48550/arxiv.2609.36910","title":"Part Size Count in Cylindric Partitions and Bijections for Small Profiles","display_name":"Part Size Count in Cylindric Partitions and Bijections for Small Profiles","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214907817","doi":"https://doi.org/10.48550/arxiv.2609.36910"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.36910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36910","pdf_url":"https://arxiv.org/pdf/2609.36910","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/2609.36910","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043540696","display_name":"Ka\u011fan Kur\u015fung\u00f6z","orcid":"https://orcid.org/0000-0002-4678-5240","observed_orcids":["https://orcid.org/0000-0002-4678-5240"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kur\u015fung\u00f6z, Ka\u011fan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040247438","display_name":"Hal\u0131\u0307me \u00d6mr\u00fcuzun Seyrek","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210104933","display_name":"Biruni University","ror":"https://ror.org/01nkhmn89","country_code":"TR","type":"education","lineage":["https://openalex.org/I4210104933"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Seyrek, Halime \u00d6mr\u00fcuzun","raw_affiliation_strings":["Faculty of Applied Sciences , Biruni University , Zeytinburnu , Is- tanbul 34015 , Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Applied Sciences , Biruni University , Zeytinburnu , Is- tanbul 34015 , Turkey","institution_ids":["https://openalex.org/I4210104933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6704000234603882,"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":0.6704000234603882,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.328900009393692,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":9.999999747378752e-05,"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/bijections","display_name":"bijections","score":0.7820000052452087},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.6859999895095825},{"id":"https://openalex.org/keywords/functional-equations","display_name":"functional equations","score":0.7879999876022339},{"id":"https://openalex.org/keywords/distinct-parts","display_name":"distinct parts","score":0.7200000286102295},{"id":"https://openalex.org/keywords/integer-partitions","display_name":"integer partitions","score":0.6769999861717224}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.987500011920929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.779699981212616},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6157000064849854},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.49630001187324524},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.44690001010894775},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.4187000095844269},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C2779820595","wikidata":"https://www.wikidata.org/wiki/Q798505","display_name":"Listing (finance)","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27399998903274536},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.36910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36910","pdf_url":"https://arxiv.org/pdf/2609.36910","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.2609.36910","doi":"https://doi.org/10.48550/arxiv.2609.36910","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.36910","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":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.36910","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.36910","pdf_url":"https://arxiv.org/pdf/2609.36910","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214907817.pdf","grobid_xml":"https://content.openalex.org/works/W7214907817.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1037264879","https://openalex.org/W1570030269","https://openalex.org/W1979825788","https://openalex.org/W1999242698","https://openalex.org/W2018270250","https://openalex.org/W2058321575","https://openalex.org/W2146590761","https://openalex.org/W2487268549","https://openalex.org/W2515532983","https://openalex.org/W2987960209","https://openalex.org/W3108946807","https://openalex.org/W4213087551","https://openalex.org/W4293428149","https://openalex.org/W4296779873","https://openalex.org/W4313598053","https://openalex.org/W4377138836","https://openalex.org/W4382138808","https://openalex.org/W4409408030","https://openalex.org/W4412454803","https://openalex.org/W4414384762","https://openalex.org/W4416050520","https://openalex.org/W6948009377"],"related_works":["https://openalex.org/W4377138836","https://openalex.org/W4416050520","https://openalex.org/W4412454803","https://openalex.org/W4213087551","https://openalex.org/W2527335087","https://openalex.org/W7097524747","https://openalex.org/W2951331564","https://openalex.org/W4293575585","https://openalex.org/W1037264879","https://openalex.org/W2738068509"],"abstract_inverted_index":{"We":[0],"first":[1],"study":[2],"the":[3,59],"part":[4,60],"size":[5,61],"statistic":[6],"in":[7],"cylindric":[8,27,44,54],"partitions,":[9],"listing":[10],"some":[11],"specializations":[12],"of":[13,29,43,52],"a":[14],"crude":[15],"but":[16],"general":[17],"formula.":[18],"Then,":[19],"we":[20,36],"establish":[21],"bijections":[22],"between":[23],"ordinary":[24],"partitions":[25,28,45],"and":[26,49],"small":[30],"profiles":[31],"with":[32],"additional":[33],"restrictions.":[34],"Lastly,":[35],"extend":[37],"earlier":[38],"formulas":[39],"for":[40],"generating":[41,56],"functions":[42],"into":[46],"distinct":[47],"parts":[48],"functional":[50],"equations":[51],"unrestricted":[53],"partition":[55],"functions,":[57],"involving":[58],"statistic.":[62]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}
