{"corpus_id":209958830,"paper_sha":"d8e743a9122145da39f70c836a8bdfbda7e63a69","doi":"10.1088/1742-6596/1294/3/032019","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2981713652,"dblp_id":null,"acl_id":null,"title":"Constructing a Nested Chain in James Abacus Diagram","year":2019,"publication_date":"2019-09-01","venue":"Journal of Physics: Conference Series","journal":{"name":"Journal of Physics: Conference Series","pages":null,"volume":"1294"},"journal_issn":null,"journal_title":null,"publication_types":["Conference"],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Physics"],"reference_count":15,"citation_count":4,"influential_citation_count":1,"is_open_access":false,"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":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"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":"James abacus diagram with e column and r rows is a combinatorial model used to represent any partition of a positive integer. In this paper, nested chain in James diagram is constructed which depended on e and r. Three forms of nested chain are found which are e < r, e > r and e = r. Then, characteristics for each form are provided. Furthermore, position numbers in each chain are then determined. In addition, a new function is established in order to determine the number of chains. Also sequences of the number of chains in nested chain are finally obtained.","claims":[{"public_id":"cl_d74454aeea04155b79472ba8c3f6de87","status":"active","text":"A nested chain is constructed in the James diagram, and its form depends on the relationship between e and r.","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_d74454aeea04155b79472ba8c3f6de87"},{"public_id":"cl_f4104a65109f52863ec7a666c89c55cd","status":"active","text":"A new function is introduced to determine the number of chains, and sequences for the number of chains are obtained.","confidence":0.94,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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