{"id":"https://openalex.org/W1676723489","doi":"https://doi.org/10.1090/s0025-5718-98-01002-3","title":"Infinite families of solutions of the equation \\binom{\ud835\udc5b}\ud835\udc58=2\\binom{\ud835\udc4e}\ud835\udc4f","display_name":"Infinite families of solutions of the equation \\binom{\ud835\udc5b}\ud835\udc58=2\\binom{\ud835\udc4e}\ud835\udc4f","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1676723489","doi":"https://doi.org/10.1090/s0025-5718-98-01002-3","mag":"1676723489"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-98-01002-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-01002-3","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-01002-3/S0025-5718-98-01002-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-01002-3/S0025-5718-98-01002-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015655109","display_name":"Pierre Goetgheluck","orcid":null},"institutions":[{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"P. Goetgheluck","raw_affiliation_strings":["Universit\u00c3\u00a9 de Paris-Sud, Math\u00c3\u00a9matiques, Bat 425, 91405 Orsay Cedex, France","Universit\u00e9 de Paris-Sud, Math\u00e9matiques, Bat 425, 91405 Orsay Cedex, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00c3\u00a9 de Paris-Sud, Math\u00c3\u00a9matiques, Bat 425, 91405 Orsay Cedex, France","institution_ids":["https://openalex.org/I102197404"]},{"raw_affiliation_string":"Universit\u00e9 de Paris-Sud, Math\u00e9matiques, Bat 425, 91405 Orsay Cedex, France","institution_ids":["https://openalex.org/I204730241"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015655109"],"corresponding_institution_ids":["https://openalex.org/I102197404","https://openalex.org/I204730241"],"apc_list":null,"apc_paid":null,"fwci":0.4762,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.55073431,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"67","issue":"224","first_page":"1727","last_page":"1733"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9995999932289124,"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9995999932289124,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8754856586456299},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.5190137624740601},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.5084027647972107},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3603144884109497},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2633205056190491},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2568624019622803}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8754856586456299},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.5190137624740601},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.5084027647972107},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3603144884109497},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2633205056190491},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2568624019622803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-98-01002-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-01002-3","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-01002-3/S0025-5718-98-01002-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-98-01002-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-98-01002-3","pdf_url":"https://www.ams.org/mcom/1998-67-224/S0025-5718-98-01002-3/S0025-5718-98-01002-3.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1676723489.pdf","grobid_xml":"https://content.openalex.org/works/W1676723489.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W45884410","https://openalex.org/W1989463534","https://openalex.org/W1998363224","https://openalex.org/W2050819248","https://openalex.org/W2052078837","https://openalex.org/W2060998417","https://openalex.org/W2739191155","https://openalex.org/W2798483379","https://openalex.org/W3159477971","https://openalex.org/W4213412932","https://openalex.org/W4251238338","https://openalex.org/W4256170887","https://openalex.org/W4403297146"],"related_works":["https://openalex.org/W1572536327","https://openalex.org/W1619654942","https://openalex.org/W4387298493","https://openalex.org/W4212980217","https://openalex.org/W3214798365","https://openalex.org/W4225635267","https://openalex.org/W2266792609","https://openalex.org/W2896451556","https://openalex.org/W4200087232","https://openalex.org/W2966298095"],"abstract_inverted_index":{"We":[0],"give":[1],"explicit":[2],"formulas":[3],"providing":[4],"two":[5],"new":[6],"infinite":[7],"families":[8],"of":[9,11],"couples":[10],"binomial":[12],"coefficients":[13],"whose":[14],"ratio":[15],"is":[16],"2.":[17]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
