{"id":"https://openalex.org/W2154740390","doi":"https://doi.org/10.37236/1097","title":"Factorial Grothendieck Polynomials","display_name":"Factorial Grothendieck Polynomials","publication_year":2006,"publication_date":"2006-08-10","ids":{"openalex":"https://openalex.org/W2154740390","doi":"https://doi.org/10.37236/1097","mag":"2154740390"},"language":"en","primary_location":{"id":"doi:10.37236/1097","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1097","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r71/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r71/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060972783","display_name":"Peter J. McNamara","orcid":"https://orcid.org/0000-0001-6111-1511"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Peter J. McNamara","raw_affiliation_strings":["Department of Mathematics and Statistics","University of Sydney, NSW 2006, Australia","University of Sydney"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Sydney, NSW 2006, Australia","institution_ids":["https://openalex.org/I129604602"]},{"raw_affiliation_string":"University of Sydney","institution_ids":["https://openalex.org/I129604602"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5060972783"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":null,"apc_paid":null,"fwci":0.9381,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.74443043,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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":1.0,"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":0.9919999837875366,"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/mathematics","display_name":"Mathematics","score":0.8996961712837219},{"id":"https://openalex.org/keywords/factorial","display_name":"Factorial","score":0.6552244424819946},{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.6179326176643372},{"id":"https://openalex.org/keywords/schur-polynomial","display_name":"Schur polynomial","score":0.5812731385231018},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5450376272201538},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.4848659932613373},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3943469524383545},{"id":"https://openalex.org/keywords/discrete-orthogonal-polynomials","display_name":"Discrete orthogonal polynomials","score":0.34258872270584106},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3363555669784546},{"id":"https://openalex.org/keywords/macdonald-polynomials","display_name":"Macdonald polynomials","score":0.3123528063297272},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.04191946983337402}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8996961712837219},{"id":"https://openalex.org/C183763347","wikidata":"https://www.wikidata.org/wiki/Q120976","display_name":"Factorial","level":2,"score":0.6552244424819946},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.6179326176643372},{"id":"https://openalex.org/C146922319","wikidata":"https://www.wikidata.org/wiki/Q4298935","display_name":"Schur polynomial","level":5,"score":0.5812731385231018},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5450376272201538},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.4848659932613373},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3943469524383545},{"id":"https://openalex.org/C52537462","wikidata":"https://www.wikidata.org/wiki/Q5282055","display_name":"Discrete orthogonal polynomials","level":3,"score":0.34258872270584106},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3363555669784546},{"id":"https://openalex.org/C171686973","wikidata":"https://www.wikidata.org/wiki/Q17098676","display_name":"Macdonald polynomials","level":4,"score":0.3123528063297272},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.04191946983337402}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1097","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1097","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r71/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1097","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1097","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r71/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2154740390.pdf","grobid_xml":"https://content.openalex.org/works/W2154740390.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W171585182","https://openalex.org/W1518468345","https://openalex.org/W1625244118","https://openalex.org/W1677701135","https://openalex.org/W1966062021","https://openalex.org/W1967764902","https://openalex.org/W1974449201","https://openalex.org/W1975605482","https://openalex.org/W1997100764","https://openalex.org/W1997526206","https://openalex.org/W2000697391","https://openalex.org/W2087792692","https://openalex.org/W2094594266","https://openalex.org/W2134984950","https://openalex.org/W2155082294","https://openalex.org/W6638968228","https://openalex.org/W6679742276"],"related_works":["https://openalex.org/W2051848833","https://openalex.org/W1565422586","https://openalex.org/W2953359705","https://openalex.org/W2217094202","https://openalex.org/W2018407410","https://openalex.org/W4302040388","https://openalex.org/W2952634831","https://openalex.org/W2952560466","https://openalex.org/W4302322159","https://openalex.org/W2325786722"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4,29],"Grothendieck":[5,19,44],"polynomials":[6,20],"indexed":[7],"by":[8],"Grassmannian":[9],"permutations":[10],"from":[11],"a":[12,37,40],"combinatorial":[13],"viewpoint.":[14],"We":[15],"introduce":[16],"the":[17,25],"factorial":[18,26],"which":[21],"are":[22],"analogues":[23],"of":[24,39],"Schur":[27],"functions,":[28],"their":[30],"properties,":[31],"and":[32],"use":[33],"them":[34],"to":[35],"produce":[36],"generalisation":[38],"Littlewood-Richardson":[41],"rule":[42],"for":[43],"polynomials.":[45]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}