Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2069711351', 'doi': 'https://doi.org/10.1007/s00026-011-0115-4', 'title': 'Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited', 'display_name': 'Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited', 'publication_year': 2011, 'publication_date': '2011-10-01', 'ids': {'openalex': 'https://openalex.org/W2069711351', 'doi': 'https://doi.org/10.1007/s00026-011-0115-4', 'mag': '2069711351'}, 'language': 'en', 'primary_location': {'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s00026-011-0115-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S138567582', 'display_name': 'Annals of Combinatorics', 'issn_l': '0218-0006', 'issn': ['0218-0006', '0219-3094'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'green', 'oa_url': 'https://hal.science/hal-00325270/document', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5032804163', 'display_name': 'Cyrille Bertelle', 'orcid': 'https://orcid.org/0000-0002-5484-161X'}, 'institutions': [], 'countries': [], 'is_corresponding': False, 'raw_author_name': 'Gérard H. E. Duchamp', 'raw_affiliation_strings': ['Institut Galilée, LIPN, UMR CNRS 7030'], 'affiliations': [{'raw_affiliation_string': 'Institut Galilée, LIPN, UMR CNRS 7030', 'institution_ids': []}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5039200724', 'display_name': 'Florent Hivert', 'orcid': 'https://orcid.org/0000-0002-7531-5985'}, 'institutions': [{'id': 'https://openalex.org/I62396329', 'display_name': 'Université de Rouen Normandie', 'ror': 'https://ror.org/03nhjew95', 'country_code': 'FR', 'type': 'education', 'lineage': ['https://openalex.org/I4210105918', 'https://openalex.org/I62396329']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Florent Hivert', 'raw_affiliation_strings': ['LITIS (Université de Rouen)'], 'affiliations': [{'raw_affiliation_string': 'LITIS (Université de Rouen)', 'institution_ids': ['https://openalex.org/I62396329']}]}, {'author_position': 'middle', 'author': {'id': 'https://openalex.org/A5051272665', 'display_name': 'Jean-Christophe Novelli', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I4210152518', 'display_name': "Laboratoire d'Informatique Gaspard-Monge", 'ror': 'https://ror.org/04t50yk91', 'country_code': 'FR', 'type': 'facility', 'lineage': ['https://openalex.org/I1294671590', 'https://openalex.org/I142631665', 'https://openalex.org/I190752583', 'https://openalex.org/I4210152518', 'https://openalex.org/I4210154111', 'https://openalex.org/I4210159245']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Jean-Christophe Novelli', 'raw_affiliation_strings': ['Institut Gaspard-Monge, Université Paris-Est, 5'], 'affiliations': [{'raw_affiliation_string': 'Institut Gaspard-Monge, Université Paris-Est, 5', 'institution_ids': ['https://openalex.org/I4210152518']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5085392129', 'display_name': 'Jean-Yves Thibon', 'orcid': 'https://orcid.org/0000-0002-8976-4044'}, 'institutions': [{'id': 'https://openalex.org/I4210152518', 'display_name': "Laboratoire d'Informatique Gaspard-Monge", 'ror': 'https://ror.org/04t50yk91', 'country_code': 'FR', 'type': 'facility', 'lineage': ['https://openalex.org/I1294671590', 'https://openalex.org/I142631665', 'https://openalex.org/I190752583', 'https://openalex.org/I4210152518', 'https://openalex.org/I4210154111', 'https://openalex.org/I4210159245']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Jean-Yves Thibon', 'raw_affiliation_strings': ['Institut Gaspard-Monge, Université Paris-Est, 5'], 'affiliations': [{'raw_affiliation_string': 'Institut Gaspard-Monge, Université Paris-Est, 5', 'institution_ids': ['https://openalex.org/I4210152518']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 2, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 2290, 'currency': 'EUR', 'value_usd': 2890, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 5.845, 'has_fulltext': True, 'fulltext_origin': 'ngrams', 'cited_by_count': 102, 'citation_normalized_percentile': {'value': 0.920635, 'is_in_top_1_percent': False, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 97, 'max': 98}, 'biblio': {'volume': '15', 'issue': '4', 'first_page': '655', 'last_page': '673'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10948', 'display_name': 'Combinatorial Mathematics and Algebraic Combinatorics', 'score': 0.9999, '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': 'Combinatorial Mathematics and Algebraic Combinatorics', 'score': 0.9999, '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/T10287', 'display_name': 'Cluster Algebras and Triangulated Categories', 'score': 0.9986, '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/T12748', 'display_name': 'Chiroptical Spectroscopy in Organic Compound Analysis', 'score': 0.9986, 'subfield': {'id': 'https://openalex.org/subfields/1607', 'display_name': 'Spectroscopy'}, 'field': {'id': 'https://openalex.org/fields/16', 'display_name': 'Chemistry'}, 'domain': {'id': 'https://openalex.org/domains/3', 'display_name': 'Physical Sciences'}}], 'keywords': [{'id': 'https://openalex.org/keywords/symmetric-function', 'display_name': 'Symmetric function', 'score': 0.8349174}, {'id': 'https://openalex.org/keywords/stanley-symmetric-function', 'display_name': 'Stanley symmetric function', 'score': 0.5903484}, {'id': 'https://openalex.org/keywords/density-functional-theory', 'display_name': 'Density-Functional Theory', 'score': 0.489487}, {'id': 'https://openalex.org/keywords/symmetric-closure', 'display_name': 'Symmetric closure', 'score': 0.45652145}, {'id': 'https://openalex.org/keywords/triple-system', 'display_name': 'Triple system', 'score': 0.43720698}], 'concepts': [{'id': 'https://openalex.org/C3746008', 'wikidata': 'https://www.wikidata.org/wiki/Q981351', 'display_name': 'Symmetric function', 'level': 2, 'score': 0.8349174}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.82158196}, {'id': 'https://openalex.org/C68797384', 'wikidata': 'https://www.wikidata.org/wiki/Q2746792', 'display_name': 'Noncommutative geometry', 'level': 2, 'score': 0.78744185}, {'id': 'https://openalex.org/C156903151', 'wikidata': 'https://www.wikidata.org/wiki/Q17102788', 'display_name': 'Ring of symmetric functions', 'level': 4, 'score': 0.6671398}, {'id': 'https://openalex.org/C177148314', 'wikidata': 'https://www.wikidata.org/wiki/Q170084', 'display_name': 'Generalization', 'level': 2, 'score': 0.65875393}, {'id': 'https://openalex.org/C171436396', 'wikidata': 'https://www.wikidata.org/wiki/Q5156499', 'display_name': 'Complete homogeneous symmetric polynomial', 'level': 5, 'score': 0.6267959}, {'id': 'https://openalex.org/C2778355321', 'wikidata': 'https://www.wikidata.org/wiki/Q17079427', 'display_name': 'Identity (music)', 'level': 2, 'score': 0.61195624}, {'id': 'https://openalex.org/C64338288', 'wikidata': 'https://www.wikidata.org/wiki/Q2235316', 'display_name': 'Elementary symmetric polynomial', 'level': 4, 'score': 0.6012538}, {'id': 'https://openalex.org/C78136718', 'wikidata': 'https://www.wikidata.org/wiki/Q7600073', 'display_name': 'Stanley symmetric function', 'level': 5, 'score': 0.5903484}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.528667}, {'id': 'https://openalex.org/C129010115', 'wikidata': 'https://www.wikidata.org/wiki/Q1298683', 'display_name': 'Power sum symmetric polynomial', 'level': 5, 'score': 0.4844687}, {'id': 'https://openalex.org/C128622974', 'wikidata': 'https://www.wikidata.org/wiki/Q849512', 'display_name': 'Symmetric group', 'level': 2, 'score': 0.45722312}, {'id': 'https://openalex.org/C167552581', 'wikidata': 'https://www.wikidata.org/wiki/Q194221', 'display_name': 'Symmetric closure', 'level': 5, 'score': 0.45652145}, {'id': 'https://openalex.org/C109385661', 'wikidata': 'https://www.wikidata.org/wiki/Q11358307', 'display_name': 'Triple system', 'level': 2, 'score': 0.43720698}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.35457405}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.25748512}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.094397426}, {'id': 'https://openalex.org/C171686973', 'wikidata': 'https://www.wikidata.org/wiki/Q17098676', 'display_name': 'Macdonald polynomials', 'level': 4, 'score': 0.07651129}, {'id': 'https://openalex.org/C24890656', 'wikidata': 'https://www.wikidata.org/wiki/Q82811', 'display_name': 'Acoustics', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C52537462', 'wikidata': 'https://www.wikidata.org/wiki/Q5282055', 'display_name': 'Discrete orthogonal polynomials', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C10628310', 'wikidata': 'https://www.wikidata.org/wiki/Q619458', 'display_name': 'Orthogonal polynomials', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C86607863', 'wikidata': 'https://www.wikidata.org/wiki/Q5275279', 'display_name': 'Difference polynomials', 'level': 3, 'score': 0.0}], 'mesh': [], 'locations_count': 9, 'locations': [{'is_oa': False, 'landing_page_url': 'https://doi.org/10.1007/s00026-011-0115-4', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S138567582', 'display_name': 'Annals of Combinatorics', 'issn_l': '0218-0006', 'issn': ['0218-0006', '0219-3094'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320186', 'host_organization_name': 'Birkhäuser', 'host_organization_lineage': ['https://openalex.org/P4310320186', 'https://openalex.org/P4310319900', 'https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Birkhäuser', 'Springer Science+Business Media', 'Springer Nature'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-00325270', 'pdf_url': 'https://hal.science/hal-00325270/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://hal.science/hal-00826640', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': False, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-00826640', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': None, 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/0809.4479', 'pdf_url': 'https://arxiv.org/pdf/0809.4479', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': None, 'pdf_url': 'https://arxiv.org/pdf/0809.4479v1.pdf', 'source': {'id': 'https://openalex.org/S4306400194', 'display_name': 'arXiv (Cornell University)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I205783295', 'host_organization_name': 'Cornell University', 'host_organization_lineage': ['https://openalex.org/I205783295'], 'host_organization_lineage_names': ['Cornell University'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.science/hal-00325270/file/ncsf7.pdf', 'pdf_url': 'https://hal.science/hal-00325270/file/ncsf7.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-00325270/file/ncsf7.pdf', 'pdf_url': 'https://hal.archives-ouvertes.fr/hal-00325270/file/ncsf7.pdf', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, {'is_oa': True, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-00325270/document', 'pdf_url': 'https://hal.archives-ouvertes.fr/hal-00325270/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': None, 'license_id': None, 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://hal.archives-ouvertes.fr/hal-00325270', 'pdf_url': 'https://hal.science/hal-00325270/document', 'source': {'id': 'https://openalex.org/S4306402512', 'display_name': 'HAL (Le Centre pour la Communication Scientifique Directe)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I1294671590', 'host_organization_name': 'Centre National de la Recherche Scientifique', 'host_organization_lineage': ['https://openalex.org/I1294671590'], 'host_organization_lineage_names': ['Centre National de la Recherche Scientifique'], 'type': 'repository'}, 'license': 'other-oa', 'license_id': 'https://openalex.org/licenses/other-oa', 'version': 'submittedVersion', 'is_accepted': False, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 20, 'referenced_works': ['https://openalex.org/W131742520', 'https://openalex.org/W1493137254', 'https://openalex.org/W1546574518', 'https://openalex.org/W1636559058', 'https://openalex.org/W1659648688', 'https://openalex.org/W1966547931', 'https://openalex.org/W1969587455', 'https://openalex.org/W1970015403', 'https://openalex.org/W2010073471', 'https://openalex.org/W2019582080', 'https://openalex.org/W2038966162', 'https://openalex.org/W2043056264', 'https://openalex.org/W2057621580', 'https://openalex.org/W2059894505', 'https://openalex.org/W2075983927', 'https://openalex.org/W2126209209', 'https://openalex.org/W2148474862', 'https://openalex.org/W4242999670', 'https://openalex.org/W4285719527', 'https://openalex.org/W4388320797'], 'related_works': ['https://openalex.org/W3045701420', 'https://openalex.org/W2962861350', 'https://openalex.org/W2949691349', 'https://openalex.org/W2949072321', 'https://openalex.org/W2901510162', 'https://openalex.org/W2061180434', 'https://openalex.org/W2028338466', 'https://openalex.org/W2009793866', 'https://openalex.org/W1966596853', 'https://openalex.org/W188141326'], 'abstract_inverted_index': {'We': [0], 'prove': [1], 'a': [2, 23], 'Cauchy': [3], 'identity': [4], 'for': [5], 'free': [6, 19], 'quasi-symmetric': [7], 'functions': [8], 'and': [9, 22], 'apply': [10], 'it': [11], 'to': [12], 'the': [13, 26], 'study': [14], 'of': [15, 25], 'various': [16], 'bases.': [17], 'A': [18], 'Weyl': [20], 'formula': [21, 28], 'generalization': [24], 'splitting': [27], 'are': [29], 'also': [30], 'discussed.': [31]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2069711351', 'counts_by_year': [{'year': 2022, 'cited_by_count': 3}, {'year': 2021, 'cited_by_count': 33}, {'year': 2020, 'cited_by_count': 33}, {'year': 2019, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 2}, {'year': 2016, 'cited_by_count': 2}, {'year': 2015, 'cited_by_count': 2}, {'year': 2014, 'cited_by_count': 3}, {'year': 2013, 'cited_by_count': 6}, {'year': 2012, 'cited_by_count': 4}], 'updated_date': '2024-09-20T00:48:34.126126', 'created_date': '2016-06-24'}