{"id":"https://openalex.org/W4415937697","doi":"https://doi.org/10.55525/tjst.1724097","title":"Combinatorial Insights into Numerical Semigroups: Rook Placements and Lah Numbers","display_name":"Combinatorial Insights into Numerical Semigroups: Rook Placements and Lah Numbers","publication_year":2025,"publication_date":"2025-11-05","ids":{"openalex":"https://openalex.org/W4415937697","doi":"https://doi.org/10.55525/tjst.1724097"},"language":"en","primary_location":{"id":"doi:10.55525/tjst.1724097","doi":"https://doi.org/10.55525/tjst.1724097","is_oa":true,"landing_page_url":"https://doi.org/10.55525/tjst.1724097","pdf_url":"https://dergipark.org.tr/en/download/article-file/4977899","source":{"id":"https://openalex.org/S4220650978","display_name":"Turkish Journal of Science and Technology","issn_l":"1308-9080","issn":["1308-9080","1308-9099"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Science and Technology","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dergipark.org.tr/en/download/article-file/4977899","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058355519","display_name":"Meral S\u00fcer","orcid":"https://orcid.org/0000-0002-5512-4305","observed_orcids":["https://orcid.org/0000-0002-5512-4305"]},"institutions":[{"id":"https://openalex.org/I32481161","display_name":"Batman University","ror":"https://ror.org/051tsqh55","country_code":"TR","type":"education","lineage":["https://openalex.org/I32481161"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Meral S\u00fcer","raw_affiliation_strings":["BATMAN \u00dcN\u0130VERS\u0130TES\u0130"],"raw_orcid":"https://orcid.org/0000-0002-5512-4305","affiliations":[{"raw_affiliation_string":"BATMAN \u00dcN\u0130VERS\u0130TES\u0130","institution_ids":["https://openalex.org/I32481161"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058355519"],"corresponding_institution_ids":["https://openalex.org/I32481161"],"apc_list":null,"apc_paid":null,"fwci":0.7551,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54085293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"21","issue":"1","first_page":"35","last_page":"45"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9717000126838684,"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":0.9717000126838684,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.02759999968111515,"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/T11428","display_name":"Advanced Mathematical Identities","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/numerical-semigroups","display_name":"numerical semigroups","score":1.0},{"id":"https://openalex.org/keywords/young-diagrams","display_name":"Young diagrams","score":0.800000011920929},{"id":"https://openalex.org/keywords/rook-polynomials","display_name":"rook polynomials","score":0.9950000047683716},{"id":"https://openalex.org/keywords/lah-numbers","display_name":"Lah numbers","score":0.9769999980926514},{"id":"https://openalex.org/keywords/ordered-partitions","display_name":"ordered partitions","score":0.9739999771118164},{"id":"https://openalex.org/keywords/rook-placements","display_name":"rook placements","score":0.6679999828338623},{"id":"https://openalex.org/keywords/combinatorial-enumeration","display_name":"combinatorial enumeration","score":0.8069999814033508}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7583000063896179},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C2779628518","wikidata":"https://www.wikidata.org/wiki/Q7069664","display_name":"Numerical semigroup","level":3,"score":0.6347000002861023},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6011999845504761},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5652999877929688},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.545799970626831},{"id":"https://openalex.org/C207405024","wikidata":"https://www.wikidata.org/wiki/Q207348","display_name":"Semigroup","level":2,"score":0.5304999947547913},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5066999793052673},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49300000071525574},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.46320000290870667},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4577000141143799},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4187999963760376},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.35040000081062317},{"id":"https://openalex.org/C54643580","wikidata":"https://www.wikidata.org/wiki/Q1005603","display_name":"Algebraic combinatorics","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C182419690","wikidata":"https://www.wikidata.org/wiki/Q205464","display_name":"Algebraic structure","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25450000166893005}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.55525/tjst.1724097","doi":"https://doi.org/10.55525/tjst.1724097","is_oa":true,"landing_page_url":"https://doi.org/10.55525/tjst.1724097","pdf_url":"https://dergipark.org.tr/en/download/article-file/4977899","source":{"id":"https://openalex.org/S4220650978","display_name":"Turkish Journal of Science and Technology","issn_l":"1308-9080","issn":["1308-9080","1308-9099"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Science and Technology","raw_type":"journal-article"},{"id":"pmh:oai:dergipark.org.tr:article/1724097","doi":null,"is_oa":false,"landing_page_url":"https://dergipark.org.tr/en/pub/tjst/article/1724097","pdf_url":null,"source":{"id":"https://openalex.org/S4220650978","display_name":"Turkish Journal of Science and Technology","issn_l":"1308-9080","issn":["1308-9080","1308-9099"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Science and Technology, Vol. 21 No. 1","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:openaccess.firat.edu.tr:11508/31144","doi":null,"is_oa":true,"landing_page_url":"https://hdl.handle.net/11508/31144","pdf_url":null,"source":{"id":"https://openalex.org/S4377196733","display_name":"DSpace - FIRAT (F\u0131rat University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I143396566","host_organization_name":"F\u0131rat University","host_organization_lineage":["https://openalex.org/I143396566"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.55525/tjst.1724097","doi":"https://doi.org/10.55525/tjst.1724097","is_oa":true,"landing_page_url":"https://doi.org/10.55525/tjst.1724097","pdf_url":"https://dergipark.org.tr/en/download/article-file/4977899","source":{"id":"https://openalex.org/S4220650978","display_name":"Turkish Journal of Science and Technology","issn_l":"1308-9080","issn":["1308-9080","1308-9099"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["tr-dizin"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Turkish Journal of Science and Technology","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415937697.pdf","grobid_xml":"https://content.openalex.org/works/W4415937697.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1514926292","https://openalex.org/W1993902519","https://openalex.org/W2034579863","https://openalex.org/W2050059900","https://openalex.org/W2243973406","https://openalex.org/W2909414648","https://openalex.org/W4237442181","https://openalex.org/W4392916232","https://openalex.org/W4408583670"],"related_works":["https://openalex.org/W7222750254","https://openalex.org/W7214802994","https://openalex.org/W4417170899","https://openalex.org/W4408583670","https://openalex.org/W2513642879","https://openalex.org/W2951105201","https://openalex.org/W286628781","https://openalex.org/W4385421419","https://openalex.org/W7027499200","https://openalex.org/W4392916232"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,12,20,36,44,66],"interplay":[4],"between":[5,89],"numerical":[6,26,81],"semigroups":[7],"and":[8,19,51,84,91],"enumerative":[9,92],"combinatorics":[10],"through":[11],"lens":[13],"of":[14,39,80],"Young":[15,32],"diagrams,":[16],"rook":[17,45],"polynomials,":[18],"Lah":[21,67],"numbers.":[22],"For":[23],"a":[24,31,62,76],"given":[25],"semigroup":[27,82],"S,":[28],"we":[29],"associate":[30],"diagram":[33,50],"constructed":[34],"from":[35],"gap":[37],"set":[38],"S.":[40],"We":[41],"then":[42],"compute":[43],"polynomial":[46],"corresponding":[47],"to":[48],"this":[49],"analyze":[52],"its":[53],"coefficients.":[54],"It":[55],"is":[56],"observed":[57],"that":[58],"these":[59],"coefficients":[60],"exhibit":[61],"strong":[63],"connection":[64],"with":[65],"numbers,":[68],"which":[69],"count":[70],"ordered":[71],"partitions.":[72],"Our":[73],"approach":[74],"introduces":[75],"new":[77],"combinatorial":[78],"interpretation":[79],"gaps":[83],"reveals":[85],"novel":[86],"structural":[87],"links":[88],"algebraic":[90],"concepts.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-13T13:42:25.865203","created_date":"2025-11-05T00:00:00"}
