{"id":"https://openalex.org/W2054833597","doi":"https://doi.org/10.1016/0097-3165(90)90006-i","title":"Reduced matrices and q-log-concavity properties of q-Stirling numbers","display_name":"Reduced matrices and q-log-concavity properties of q-Stirling numbers","publication_year":1990,"publication_date":"1990-05-01","ids":{"openalex":"https://openalex.org/W2054833597","doi":"https://doi.org/10.1016/0097-3165(90)90006-i","mag":"2054833597"},"language":"en","primary_location":{"id":"doi:10.1016/0097-3165(90)90006-i","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0097-3165(90)90006-i","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Theory, Series A","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089292335","display_name":"Pierre Leroux","orcid":null},"institutions":[{"id":"https://openalex.org/I159129438","display_name":"Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al","ror":"https://ror.org/002rjbv21","country_code":"CA","type":"education","lineage":["https://openalex.org/I159129438","https://openalex.org/I49663120"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Pierre Leroux","raw_affiliation_strings":["D\u00e9partement de math\u00e9matiques et d'informatique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, C.P. 8888, Succ. A, Montr\u00e9al, Qu\u00e9bec, Canada H3C 3P8","D\u00e9partement de Math\u00e9matiques et d'Informatique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, C.P. 8888 succ. A, Montr\u00e9al, Qu\u00e9bec, Canada H3C 3P8"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de math\u00e9matiques et d'informatique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, C.P. 8888, Succ. A, Montr\u00e9al, Qu\u00e9bec, Canada H3C 3P8","institution_ids":["https://openalex.org/I159129438"]},{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques et d'Informatique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, C.P. 8888 succ. A, Montr\u00e9al, Qu\u00e9bec, Canada H3C 3P8","institution_ids":["https://openalex.org/I159129438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089292335"],"corresponding_institution_ids":["https://openalex.org/I159129438"],"apc_list":{"value":3320,"currency":"USD","value_usd":3320},"apc_paid":null,"fwci":8.511,"has_fulltext":false,"cited_by_count":96,"citation_normalized_percentile":{"value":0.99243243,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"54","issue":"1","first_page":"64","last_page":"84"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991999864578247,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stirling-numbers-of-the-second-kind","display_name":"Stirling numbers of the second kind","score":0.8489428758621216},{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.8269268274307251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7356184720993042},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-first-kind","display_name":"Stirling numbers of the first kind","score":0.6672117710113525},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.6457209587097168},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6383199691772461},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.6217685341835022},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.6143348217010498},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5305346250534058},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.5175858736038208},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.506618082523346},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4852199852466583},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46460264921188354},{"id":"https://openalex.org/keywords/binomial-theorem","display_name":"Binomial theorem","score":0.4602111876010895},{"id":"https://openalex.org/keywords/stirling-engine","display_name":"Stirling engine","score":0.44816893339157104},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42482882738113403},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.4235353469848633},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.14099571108818054},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09091448783874512},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07427293062210083}],"concepts":[{"id":"https://openalex.org/C2284495","wikidata":"https://www.wikidata.org/wiki/Q2601117","display_name":"Stirling numbers of the second kind","level":2,"score":0.8489428758621216},{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.8269268274307251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7356184720993042},{"id":"https://openalex.org/C93765064","wikidata":"https://www.wikidata.org/wiki/Q2657556","display_name":"Stirling numbers of the first kind","level":3,"score":0.6672117710113525},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.6457209587097168},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6383199691772461},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.6217685341835022},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.6143348217010498},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5305346250534058},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.5175858736038208},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.506618082523346},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4852199852466583},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46460264921188354},{"id":"https://openalex.org/C180099792","wikidata":"https://www.wikidata.org/wiki/Q26708","display_name":"Binomial theorem","level":2,"score":0.4602111876010895},{"id":"https://openalex.org/C27134321","wikidata":"https://www.wikidata.org/wiki/Q186212","display_name":"Stirling engine","level":2,"score":0.44816893339157104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42482882738113403},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.4235353469848633},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.14099571108818054},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09091448783874512},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07427293062210083},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0097-3165(90)90006-i","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0097-3165(90)90006-i","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Combinatorial Theory, Series A","raw_type":"journal-article"},{"id":"pmh:oai:conservancy.umn.edu:11299/4969","is_oa":false,"landing_page_url":"http://purl.umn.edu/4969","pdf_url":null,"source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1976600678","https://openalex.org/W1979504938","https://openalex.org/W1985965909","https://openalex.org/W1997396462","https://openalex.org/W2043609086","https://openalex.org/W2047602652","https://openalex.org/W2048235559","https://openalex.org/W2068045918","https://openalex.org/W2072173760","https://openalex.org/W2086048413","https://openalex.org/W2086197284","https://openalex.org/W2091216084","https://openalex.org/W2093824255","https://openalex.org/W2094042760","https://openalex.org/W2134984950","https://openalex.org/W6668587414"],"related_works":["https://openalex.org/W62220391","https://openalex.org/W2025230592","https://openalex.org/W4289083088","https://openalex.org/W2980443534","https://openalex.org/W2908261864","https://openalex.org/W3147212843","https://openalex.org/W4293439290","https://openalex.org/W2145934284","https://openalex.org/W2022182642","https://openalex.org/W2054833597"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}