Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2798880819', 'doi': 'https://doi.org/10.46298/dmtcs.2722', 'title': 'Application of graph combinatorics to rational identities of type $A^\\ast$', 'display_name': 'Application of graph combinatorics to rational identities of type $A^\\ast$', 'publication_year': 2009, 'publication_date': '2009-01-01', 'ids': {'openalex': 'https://openalex.org/W2798880819', 'doi': 'https://doi.org/10.46298/dmtcs.2722', 'mag': '2798880819'}, 'language': 'fr', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.46298/dmtcs.2722', 'pdf_url': 'https://dmtcs.episciences.org/2722/pdf', 'source': {'id': 'https://openalex.org/S200334879', 'display_name': 'Discrete Mathematics & Theoretical Computer Science', 'issn_l': '1365-8050', 'issn': ['1365-8050', '1462-7264'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4328141799', 'host_organization_name': 'French association', 'host_organization_lineage': ['https://openalex.org/P4328141799'], 'host_organization_lineage_names': ['French association'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'diamond', 'oa_url': 'https://dmtcs.episciences.org/2722/pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5002032638', 'display_name': 'Adrien Boussicault', '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/I4210145102', 'https://openalex.org/I4210152518', 'https://openalex.org/I4210154111', 'https://openalex.org/I4210159245']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Adrien Boussicault', 'raw_affiliation_strings': ["Laboratoire d'Informatique Gaspard-Monge"], 'affiliations': [{'raw_affiliation_string': "Laboratoire d'Informatique Gaspard-Monge", 'institution_ids': ['https://openalex.org/I4210152518']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5086317606', 'display_name': 'Valentin Féray', 'orcid': 'https://orcid.org/0000-0002-9060-0696'}, '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/I4210145102', 'https://openalex.org/I4210152518', 'https://openalex.org/I4210154111', 'https://openalex.org/I4210159245']}], 'countries': ['FR'], 'is_corresponding': False, 'raw_author_name': 'Valentin Féray', 'raw_affiliation_strings': ["Laboratoire d'Informatique Gaspard-Monge"], 'affiliations': [{'raw_affiliation_string': "Laboratoire d'Informatique Gaspard-Monge", 'institution_ids': ['https://openalex.org/I4210152518']}]}], 'institution_assertions': [], 'countries_distinct_count': 1, 'institutions_distinct_count': 1, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': {'value': 0, 'currency': 'USD', 'value_usd': 0, 'provenance': 'doaj'}, 'apc_paid': None, 'fwci': 0.0, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 0, 'citation_normalized_percentile': {'value': 0.0, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 0, 'max': 64}, 'biblio': {'volume': 'DMTCS Proceedings vol. AK,...', 'issue': 'Proceedings', 'first_page': None, 'last_page': None}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T10948', 'display_name': 'Advanced Combinatorial Mathematics', 'score': 0.9998, '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': 0.9998, '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/T10588', 'display_name': 'Mathematical Dynamics and Fractals', 'score': 0.9898, 'subfield': {'id': 'https://openalex.org/subfields/2610', 'display_name': 'Mathematical Physics'}, '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/T12536', 'display_name': 'Topological and Geometric Data Analysis', 'score': 0.9879, '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': [], 'concepts': [{'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8052779}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.75361097}, {'id': 'https://openalex.org/C187834632', 'wikidata': 'https://www.wikidata.org/wiki/Q188804', 'display_name': 'Factorization', 'level': 2, 'score': 0.49957228}, {'id': 'https://openalex.org/C75190567', 'wikidata': 'https://www.wikidata.org/wiki/Q41237', 'display_name': 'Rational function', 'level': 2, 'score': 0.45740652}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.33627462}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.116247505}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.087755054}], 'mesh': [], 'locations_count': 4, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.46298/dmtcs.2722', 'pdf_url': 'https://dmtcs.episciences.org/2722/pdf', 'source': {'id': 'https://openalex.org/S200334879', 'display_name': 'Discrete Mathematics & Theoretical Computer Science', 'issn_l': '1365-8050', 'issn': ['1365-8050', '1462-7264'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4328141799', 'host_organization_name': 'French association', 'host_organization_lineage': ['https://openalex.org/P4328141799'], 'host_organization_lineage_names': ['French association'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://hal.inria.fr/hal-01185414', 'pdf_url': 'https://inria.hal.science/hal-01185414/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': True, 'landing_page_url': 'https://hal.inria.fr/hal-01185414/file/dmAK0119.pdf', 'pdf_url': 'https://hal.inria.fr/hal-01185414/file/dmAK0119.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.inria.fr/hal-01185414/document', 'pdf_url': 'https://hal.inria.fr/hal-01185414/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://doi.org/10.46298/dmtcs.2722', 'pdf_url': 'https://dmtcs.episciences.org/2722/pdf', 'source': {'id': 'https://openalex.org/S200334879', 'display_name': 'Discrete Mathematics & Theoretical Computer Science', 'issn_l': '1365-8050', 'issn': ['1365-8050', '1462-7264'], 'is_oa': True, 'is_in_doaj': True, 'is_core': True, 'host_organization': 'https://openalex.org/P4328141799', 'host_organization_name': 'French association', 'host_organization_lineage': ['https://openalex.org/P4328141799'], 'host_organization_lineage_names': ['French association'], 'type': 'journal'}, 'license': 'cc-by', 'license_id': 'https://openalex.org/licenses/cc-by', 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 11, 'referenced_works': ['https://openalex.org/W1557033434', 'https://openalex.org/W1996008071', 'https://openalex.org/W2021355739', 'https://openalex.org/W2057653226', 'https://openalex.org/W2060870403', 'https://openalex.org/W2134976318', 'https://openalex.org/W2341480311', 'https://openalex.org/W2743033432', 'https://openalex.org/W2798588639', 'https://openalex.org/W3102179705', 'https://openalex.org/W4293267979'], 'related_works': ['https://openalex.org/W4245490552', 'https://openalex.org/W4225152035', 'https://openalex.org/W3002753104', 'https://openalex.org/W2911598644', 'https://openalex.org/W2077600819', 'https://openalex.org/W2061531152', 'https://openalex.org/W2042127053', 'https://openalex.org/W2007980826', 'https://openalex.org/W1979597421', 'https://openalex.org/W1587224694'], 'abstract_inverted_index': {'To': [0], 'a': [1, 30, 73, 89, 98], 'word': [2], '$w$,': [3, 104], 'we': [4, 46], 'associate': [5], 'the': [6, 39, 49, 64, 67, 80, 86, 93], 'rational': [7, 61, 81], 'function': [8, 82], '$\\Psi_w': [9, 110], '=': [10, 111], '\\prod': [11, 112], '(x_{w_i}': [12, 113], '-': [13, 114], 'x_{w_{i+1}})^{-1}$.': [14, 115], 'The': [15, 41], 'main': [16], 'object,': [17], 'introduced': [18], 'by': [19, 35], 'C.': [20, 120], 'Greene': [21, 121], 'to': [22, 26, 58], 'generalize': [23], 'identities': [24], 'linked': [25], 'Murnaghan-Nakayama': [27], 'rule,': [28], 'is': [29], 'sum': [31], 'of': [32, 38, 43, 52, 66, 79, 85, 92, 97], 'its': [33], 'images': [34, 138], 'certain': [36], 'permutations': [37, 44, 141, 147], 'variables.': [40, 143], 'sets': [42], 'that': [45], 'consider': [47], 'are': [48], 'linear': [50], 'extensions': [51, 151], 'oriented': [53], 'graphs.': [54], 'We': [55, 70], 'explain': [56], 'how': [57], 'compute': [59], 'this': [60], 'function,': [62], 'using': [63], 'combinatorics': [65], 'graph': [68, 94], '$G$.': [69, 170], 'also': [71], 'establish': [72], 'link': [74], 'between': [75], 'an': [76], 'algebraic': [77], 'property': [78, 91], '(the': [83, 95], 'factorization': [84], 'numerator)': [87], 'and': [88], 'combinatorial': [90], 'existence': [96], 'disconnecting': [99], 'chain).': [100], 'À': [101], 'un': [102, 174], 'mot': [103], 'nous': [105], 'associons': [106], 'la': [107, 129, 166, 181], 'fonction': [108, 161, 182], 'rationnelle': [109, 162, 183], "L'objet": [116], 'principal,': [117], 'introduit': [118], 'par': [119, 139], 'pour': [122], 'généraliser': [123], 'des': [124, 142, 153], 'identités': [125], 'rationnelles': [126], 'liées': [127], 'à': [128, 163], 'règle': [130], 'de': [131, 136, 146, 165, 180], 'Murnaghan-Nakayama,': [132], 'est': [133], 'une': [134, 177, 189], 'somme': [135], 'ses': [137], 'certaines': [140], 'Les': [144], 'ensembles': [145], 'considérés': [148], 'sont': [149], 'les': [150], 'linéaires': [152], 'graphes': [154], 'orientés.': [155], 'Nous': [156, 171], 'expliquons': [157], 'comment': [158], 'calculer': [159], 'cette': [160], 'partir': [164], 'combinatoire': [167, 191], 'du': [168, 186, 192], 'graphe': [169, 193], 'établissons': [172], 'ensuite': [173], 'lien': [175], 'entre': [176], 'propriété': [178, 190], 'algébrique': [179], '(la': [184], 'factorisation': [185], 'numérateur)': [187], 'et': [188], "(l'existence": [194], "d'une": [195], 'chaîne': [196], 'le': [197], 'déconnectant).': [198]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2798880819', 'counts_by_year': [], 'updated_date': '2025-01-07T07:06:55.788822', 'created_date': '2018-05-07'}