Publication Information

{'id': 'https://openalex.org/W3105495689', 'doi': 'https://doi.org/10.1186/s40687-017-0107-z', 'title': 'Fourientations and the Tutte polynomial', 'display_name': 'Fourientations and the Tutte polynomial', 'publication_year': 2017, 'publication_date': '2017-05-04', 'ids': {'openalex': 'https://openalex.org/W3105495689', 'doi': 'https://doi.org/10.1186/s40687-017-0107-z', 'mag': '3105495689'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1186/s40687-017-0107-z', 'pdf_url': 'https://link.springer.com/content/pdf/10.1186%2Fs40687-017-0107-z.pdf', 'source': {'id': 'https://openalex.org/S2737856571', 'display_name': 'Research in the Mathematical Sciences', 'issn_l': '2197-9847', 'issn': ['2197-9847', '2522-0144'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], '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': ['arxiv', 'crossref', 'datacite'], 'open_access': {'is_oa': True, 'oa_status': 'hybrid', 'oa_url': 'https://link.springer.com/content/pdf/10.1186%2Fs40687-017-0107-z.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5066800852', 'display_name': 'Spencer Backman', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I135140700', 'display_name': 'University of Bonn', 'ror': 'https://ror.org/041nas322', 'country_code': 'DE', 'type': 'education', 'lineage': ['https://openalex.org/I135140700']}], 'countries': ['DE'], 'is_corresponding': False, 'raw_author_name': 'Spencer Backman', 'raw_affiliation_strings': ['Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany'], 'affiliations': [{'raw_affiliation_string': 'Hausdorff Center for Mathematics, University of Bonn, Bonn, Germany', 'institution_ids': ['https://openalex.org/I135140700']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5001123654', 'display_name': 'Sam Hopkins', 'orcid': None}, 'institutions': [{'id': 'https://openalex.org/I63966007', 'display_name': 'Massachusetts Institute of Technology', 'ror': 'https://ror.org/042nb2s44', 'country_code': 'US', 'type': 'education', 'lineage': ['https://openalex.org/I63966007']}], 'countries': ['US'], 'is_corresponding': True, 'raw_author_name': 'Sam Hopkins', 'raw_affiliation_strings': ['Massachusetts Institute of Technology, Cambridge, MA, USA'], 'affiliations': [{'raw_affiliation_string': 'Massachusetts Institute of Technology, Cambridge, MA, USA', 'institution_ids': ['https://openalex.org/I63966007']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 2, 'corresponding_author_ids': ['https://openalex.org/A5001123654'], 'corresponding_institution_ids': ['https://openalex.org/I63966007'], 'apc_list': {'value': 2790, 'currency': 'EUR', 'value_usd': 3590, 'provenance': 'doaj'}, 'apc_paid': {'value': 2790, 'currency': 'EUR', 'value_usd': 3590, 'provenance': 'doaj'}, 'fwci': 2.462, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 13, 'citation_normalized_percentile': {'value': 0.871304, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 87, 'max': 88}, 'biblio': {'volume': '4', 'issue': '1', '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': 0.9991, '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': 0.9991, '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/T12536', 'display_name': 'Topological and Geometric Data Analysis', 'score': 0.9948, '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'}}, {'id': 'https://openalex.org/T12069', 'display_name': 'Commutative Algebra and Its Applications', 'score': 0.9903, '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'}}], 'keywords': [{'id': 'https://openalex.org/keywords/tutte-polynomial', 'display_name': 'Tutte polynomial', 'score': 0.8117237}, {'id': 'https://openalex.org/keywords/chromatic-polynomial', 'display_name': 'Chromatic polynomial', 'score': 0.56673384}], 'concepts': [{'id': 'https://openalex.org/C14447369', 'wikidata': 'https://www.wikidata.org/wiki/Q7857002', 'display_name': 'Tutte polynomial', 'level': 5, 'score': 0.8117237}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.76272625}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7484275}, {'id': 'https://openalex.org/C126385604', 'wikidata': 'https://www.wikidata.org/wiki/Q1087609', 'display_name': 'Chromatic polynomial', 'level': 3, 'score': 0.56673384}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.49394923}, {'id': 'https://openalex.org/C199479865', 'wikidata': 'https://www.wikidata.org/wiki/Q205966', 'display_name': 'Riemann hypothesis', 'level': 2, 'score': 0.49304268}, {'id': 'https://openalex.org/C207043602', 'wikidata': 'https://www.wikidata.org/wiki/Q266237', 'display_name': 'Algebraic curve', 'level': 2, 'score': 0.48808062}, {'id': 'https://openalex.org/C90119067', 'wikidata': 'https://www.wikidata.org/wiki/Q43260', 'display_name': 'Polynomial', 'level': 2, 'score': 0.48076722}, {'id': 'https://openalex.org/C132525143', 'wikidata': 'https://www.wikidata.org/wiki/Q141488', 'display_name': 'Graph', 'level': 2, 'score': 0.46774724}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.42781782}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.16100022}, {'id': 'https://openalex.org/C203776342', 'wikidata': 'https://www.wikidata.org/wiki/Q1378376', 'display_name': 'Line graph', 'level': 3, 'score': 0.09823823}, {'id': 'https://openalex.org/C22149727', 'wikidata': 'https://www.wikidata.org/wiki/Q7940747', 'display_name': 'Voltage graph', 'level': 4, 'score': 0.06926298}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1186/s40687-017-0107-z', 'pdf_url': 'https://link.springer.com/content/pdf/10.1186%2Fs40687-017-0107-z.pdf', 'source': {'id': 'https://openalex.org/S2737856571', 'display_name': 'Research in the Mathematical Sciences', 'issn_l': '2197-9847', 'issn': ['2197-9847', '2522-0144'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], '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': 'http://arxiv.org/abs/1503.05885', 'pdf_url': 'http://arxiv.org/pdf/1503.05885', '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': 'http://hdl.handle.net/1721.1/117000', 'pdf_url': 'https://dspace.mit.edu/bitstream/1721.1/117000/1/40687_2017_Article_107.pdf', 'source': {'id': 'https://openalex.org/S4306400425', 'display_name': 'DSpace@MIT (Massachusetts Institute of Technology)', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I63966007', 'host_organization_name': 'Massachusetts Institute of Technology', 'host_organization_lineage': ['https://openalex.org/I63966007'], 'host_organization_lineage_names': ['Massachusetts Institute of Technology'], 'type': 'repository'}, '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://arxiv.org/abs/1503.05885', 'pdf_url': 'https://arxiv.org/pdf/1503.05885', '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': False, 'landing_page_url': 'https://api.datacite.org/dois/10.48550/arxiv.1503.05885', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S4393179698', 'display_name': 'DataCite API', 'issn_l': None, 'issn': None, 'is_oa': True, 'is_in_doaj': False, 'is_core': False, 'host_organization': 'https://openalex.org/I4210145204', 'host_organization_name': 'DataCite', 'host_organization_lineage': ['https://openalex.org/I4210145204'], 'host_organization_lineage_names': ['DataCite'], 'type': 'metadata'}, 'license': None, 'license_id': None, 'version': None}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1186/s40687-017-0107-z', 'pdf_url': 'https://link.springer.com/content/pdf/10.1186%2Fs40687-017-0107-z.pdf', 'source': {'id': 'https://openalex.org/S2737856571', 'display_name': 'Research in the Mathematical Sciences', 'issn_l': '2197-9847', 'issn': ['2197-9847', '2522-0144'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310319965', 'host_organization_name': 'Springer Nature', 'host_organization_lineage': ['https://openalex.org/P4310319965'], 'host_organization_lineage_names': ['Springer Nature'], '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': [{'funder': 'https://openalex.org/F4320306076', 'funder_display_name': 'National Science Foundation', 'award_id': '1122374'}], 'datasets': [], 'versions': ['https://openalex.org/W1912995418', 'https://openalex.org/W3105495689'], 'referenced_works_count': 73, 'referenced_works': ['https://openalex.org/W139496587', 'https://openalex.org/W1485445902', 'https://openalex.org/W1497878978', 'https://openalex.org/W1511341063', 'https://openalex.org/W1537258143', 'https://openalex.org/W1556934096', 'https://openalex.org/W1595605524', 'https://openalex.org/W1597381512', 'https://openalex.org/W1599197882', 'https://openalex.org/W1602252920', 'https://openalex.org/W1718366070', 'https://openalex.org/W1830067456', 'https://openalex.org/W1843028771', 'https://openalex.org/W1964453615', 'https://openalex.org/W1969664066', 'https://openalex.org/W1971911032', 'https://openalex.org/W1980309464', 'https://openalex.org/W1981244742', 'https://openalex.org/W1983667974', 'https://openalex.org/W1991917222', 'https://openalex.org/W1993292446', 'https://openalex.org/W1995114112', 'https://openalex.org/W1995852086', 'https://openalex.org/W1997872836', 'https://openalex.org/W1999562295', 'https://openalex.org/W2014384230', 'https://openalex.org/W2017361509', 'https://openalex.org/W2017373798', 'https://openalex.org/W2029787168', 'https://openalex.org/W2031912601', 'https://openalex.org/W2037190943', 'https://openalex.org/W2038677116', 'https://openalex.org/W2039415399', 'https://openalex.org/W2049916150', 'https://openalex.org/W2050285673', 'https://openalex.org/W2055584434', 'https://openalex.org/W2055585984', 'https://openalex.org/W2066653142', 'https://openalex.org/W2081659888', 'https://openalex.org/W2082995593', 'https://openalex.org/W2083387674', 'https://openalex.org/W2110539170', 'https://openalex.org/W2115732351', 'https://openalex.org/W2140545974', 'https://openalex.org/W2142533317', 'https://openalex.org/W2147534265', 'https://openalex.org/W2148260769', 'https://openalex.org/W2154568177', 'https://openalex.org/W2157837124', 'https://openalex.org/W2158604375', 'https://openalex.org/W2168359188', 'https://openalex.org/W2218040560', 'https://openalex.org/W2230760380', 'https://openalex.org/W2243948417', 'https://openalex.org/W2254723345', 'https://openalex.org/W2314361409', 'https://openalex.org/W2597427573', 'https://openalex.org/W2608666998', 'https://openalex.org/W2924832700', 'https://openalex.org/W2949636768', 'https://openalex.org/W2963913299', 'https://openalex.org/W2964022551', 'https://openalex.org/W2964136011', 'https://openalex.org/W2994578641', 'https://openalex.org/W3037444656', 'https://openalex.org/W3037545555', 'https://openalex.org/W3105075611', 'https://openalex.org/W4206077821', 'https://openalex.org/W4255131284', 'https://openalex.org/W4294328963', 'https://openalex.org/W4294589747', 'https://openalex.org/W4300892468', 'https://openalex.org/W94268855'], 'related_works': ['https://openalex.org/W593587541', 'https://openalex.org/W4302506957', 'https://openalex.org/W4211170257', 'https://openalex.org/W2964638337', 'https://openalex.org/W2953032778', 'https://openalex.org/W2527934888', 'https://openalex.org/W2073184325', 'https://openalex.org/W2032055415', 'https://openalex.org/W2026073766', 'https://openalex.org/W1531965102'], 'abstract_inverted_index': {'A': [0], 'fourientation': [1, 95, 121], 'of': [2, 11, 39, 45, 62, 92, 103, 120, 178], 'a': [3, 6, 29, 36, 111], 'graph': [4, 13], 'is': [5], 'choice': [7], 'for': [8, 78, 136, 145, 164, 198], 'each': [9], 'edge': [10, 18], 'the': [12, 33, 40, 63, 118, 150, 154, 203], 'whether': [14], 'to': [15, 123, 139, 149, 168, 181], 'orient': [16], 'that': [17, 56], 'in': [19, 49], 'either': [20], 'direction,': [21], 'leave': [22], 'it': [23], 'unoriented,': [24], 'or': [25], 'biorient': [26], 'it.': [27], 'Fixing': [28], 'total': [30, 165], 'order': [31], 'on': [32], 'edges': [34], 'and': [35, 47, 82, 115, 132, 141, 143, 153, 157, 184, 202], 'reference': [37], 'orientation': [38], 'graph,': [41], 'we': [42], 'investigate': [43], 'properties': [44], 'cuts': [46], 'cycles': [48], 'fourientations': [50, 137, 179], 'which': [51, 124], 'give': [52], 'trivariate': [53], 'generating': [54], 'functions': [55], 'are': [57], 'generalized': [58, 99], 'Tutte': [59, 100], 'polynomial': [60, 101], 'evaluations': [61, 102], 'form': [64], '\\[(k+m)^{n-1}(k+l)^gT\\left(\\frac{\\alpha': [65], 'k': [66, 72], '+': [67, 70, 73, 75], '\\beta': [68], 'l': [69, 74], 'm}{k+m},\\frac{\\gamma': [71], '\\delta': [76, 84], 'm}{k+l}\\right)\\]': [77], '$\\alpha,\\gamma': [79], '\\in': [80, 85], '\\{0,1,2\\}$': [81], '$\\beta,': [83], '\\{0,1\\}$.': [86], 'We': [87, 106, 171], 'introduce': [88], 'an': [89], 'intersection': [90], 'lattice': [91], '64': [93], 'cut-cycle': [94], 'classes': [96, 122, 177], 'enumerated': [97], 'by': [98, 173], 'this': [104], 'form.': [105], 'prove': [107], 'these': [108, 176], 'enumerations': [109], 'using': [110], 'single': [112], 'deletion-contraction': [113, 126], 'argument': [114, 127], 'classify': [116], 'axiomatically': [117], 'set': [119], 'our': [125], 'applies.': [128], 'This': [129], 'work': [130], 'unifies': [131], 'extends': [133], 'earlier': [134], 'results': [135, 144, 163], 'due': [138, 148, 167], 'Gessel': [140], 'Sagan,': [142], 'partial': [146], 'orientations': [147, 166], 'first': [151], 'author,': [152], 'second': [155], 'author': [156], 'David': [158], 'Perkinson,': [159], 'as': [160, 162], 'well': [161], 'many': [169], 'authors.': [170], 'conclude': [172], 'describing': [174], 'how': [175], 'relate': [180], 'geometric,': [182], 'combinatorial,': [183], 'algebraic': [185], 'objects': [186], 'including': [187], 'bigraphical': [188], 'arrangements,': [189], 'cycle-cocycle': [190], 'reversal': [191], 'systems,': [192], 'graphic': [193], 'Lawrence': [194], 'ideals,': [195], 'Riemann-Roch': [196], 'theory': [197], 'graphs,': [199], 'zonotopal': [200], 'algebras,': [201], 'reliability': [204], 'polynomial.': [205]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W3105495689', 'counts_by_year': [{'year': 2023, 'cited_by_count': 3}, {'year': 2021, 'cited_by_count': 1}, {'year': 2020, 'cited_by_count': 2}, {'year': 2019, 'cited_by_count': 2}, {'year': 2018, 'cited_by_count': 1}, {'year': 2017, 'cited_by_count': 3}, {'year': 2016, 'cited_by_count': 1}], 'updated_date': '2024-12-16T14:34:11.332556', 'created_date': '2020-11-23'}