{"corpus_id":269957283,"paper_sha":"df70c150bdaa2ea5a2af396f42c0b6ea127d2543","doi":"10.2298/fil2320917y","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":null,"dblp_id":null,"acl_id":null,"title":"Some binomial identities related to the Catalan triangles and the halves of the Pascal matrix","year":2023,"publication_date":null,"venue":"Filomat","journal":{"name":"Filomat","pages":null,"volume":null},"journal_issn":null,"journal_title":null,"publication_types":["JournalArticle"],"pubmed_pub_types":null,"s2_fields_of_study":[],"reference_count":23,"citation_count":2,"influential_citation_count":0,"is_open_access":true,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"http://www.doiserbia.nb.rs/ft.aspx?id=0354-51802320917Y","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/df70c150bdaa2ea5a2af396f42c0b6ea127d2543","s2_open_access_license":"other-oa","s2_open_access_status":"GOLD","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"In this paper, five binomial sums with two additional parameters are shown to\n be equipollent by using the Riordan array method and the generalized Catalan\n matrices, as well as the halves of the Pascal matrix.","claims":[{"public_id":"cl_a35e9f2b27ea27ed75626a4520e69687","status":"active","text":"Five binomial sums with two additional parameters are shown to be equipollent.","confidence":0.98,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_a35e9f2b27ea27ed75626a4520e69687"},{"public_id":"cl_5151426148c6c7e6d67a40c6ef38d959","status":"active","text":"The equivalence is established using the Riordan array method, the generalized Catalan matrices, and the halves of the Pascal matrix.","confidence":0.97,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_5151426148c6c7e6d67a40c6ef38d959"}],"concepts":[{"public_id":"co_10a2c472f6aa7453336c381e8941b28e","status":"active","name":"Catalan triangles","description":"Triangular arrays of Catalan-number-related coefficients used in combinatorial identities.","types":["combinatorial array"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_10a2c472f6aa7453336c381e8941b28e"},{"public_id":"co_19f23f5cea697e5f93cf78f4c50ae7cc","status":"active","name":"halves of the Pascal matrix","description":"The left and right half-matrix decompositions derived from the Pascal matrix.","types":["matrix"],"aliases":["Pascal matrix halves"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_19f23f5cea697e5f93cf78f4c50ae7cc"},{"public_id":"co_1f05a8640357d884934dba37343df774","status":"active","name":"Pascal matrix","description":"The infinite matrix of binomial coefficients.","types":["matrix"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_1f05a8640357d884934dba37343df774"},{"public_id":"co_34e15d5926307602e249f4f098f8c9dd","status":"active","name":"equipollent","description":"Having the same value or being mutually equivalent in the sense used for the binomial identities.","types":["property"],"aliases":["equivalent"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_34e15d5926307602e249f4f098f8c9dd"},{"public_id":"co_4e81c36468cc9fc730c5c0a8cd66c355","status":"active","name":"generalized Catalan matrices","description":"Matrix forms associated with generalized Catalan-number structures.","types":["matrix"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_4e81c36468cc9fc730c5c0a8cd66c355"},{"public_id":"co_6568c8438dcf3b2d1411597b01a724ed","status":"active","name":"binomial sums with two additional parameters","description":"Binomial summation identities that include two extra parameters in their terms.","types":["mathematical expression"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_6568c8438dcf3b2d1411597b01a724ed"},{"public_id":"co_97d38210ca59f25002017f6e99a376b5","status":"active","name":"binomial identities","description":"Identities involving binomial coefficients and related summations.","types":["mathematical identity"],"aliases":[],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_97d38210ca59f25002017f6e99a376b5"},{"public_id":"co_fa53627ceb0befb0f2b48445105146ae","status":"active","name":"Riordan array method","description":"A combinatorial matrix method used to derive and prove identities.","types":["method"],"aliases":["Riordan arrays"],"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/concepts/co_fa53627ceb0befb0f2b48445105146ae"}],"external_ids":{"DOI":"10.2298/fil2320917y","ArXiv":null,"PubMed":null,"PubMedCentral":null,"MAG":null,"DBLP":null,"ACL":null},"open_access":{"is_open_access":true,"pdf_url":"http://www.doiserbia.nb.rs/ft.aspx?id=0354-51802320917Y","landing_url":"https://www.semanticscholar.org/paper/df70c150bdaa2ea5a2af396f42c0b6ea127d2543","source":"semantic_scholar","pdf_url_source":"semantic_scholar_open_access_pdf","license":"other-oa","status":"GOLD","reason":null},"reference_availability":{"status":"available","references_indexed":true,"full_text_available":false,"full_text_source":null,"count_basis":"semantic_scholar_metadata","extraction_status":"not_applicable","reason":null},"source":{"provider":"episteme2","base_corpus":"semantic_scholar_dump","freshness_mode":"unknown","basis":["semantic_scholar_metadata","postgres_metadata"],"limits":["paper metadata is based on indexed upstream scholarly datasets","claims and concepts are available only for extracted papers","absence of claims or concepts means no extracted graph data is available in this response"],"status":"available","degraded":false,"degraded_reasons":[],"diagnostics":{"status":"available","degraded":false,"degraded_reasons":[],"metadata_status":"available","graph_status":"available","abstract_status":"available"},"source_flags":1},"paper_id":633868,"paper_uid":"24cee2a6-b46f-4b62-af03-ad18c524ec19","canonical_identity":{"paper_id":633868,"paper_uid":"24cee2a6-b46f-4b62-af03-ad18c524ec19","identity_status":"available","lookup_basis":"semantic_scholar_external_id","compatibility_path":"corpus_id"},"url":"https://sah.borca.ai/papers/269957283"}