Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W2166469367', 'doi': 'https://doi.org/10.2140/gt.2010.14.2243', 'title': 'Twist-rigid Coxeter groups', 'display_name': 'Twist-rigid Coxeter groups', 'publication_year': 2010, 'publication_date': '2010-10-28', 'ids': {'openalex': 'https://openalex.org/W2166469367', 'doi': 'https://doi.org/10.2140/gt.2010.14.2243', 'mag': '2166469367'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/gt.2010.14.2243', 'pdf_url': 'https://msp.org/gt/2010/14-4/gt-v14-n4-p10-s.pdf', 'source': {'id': 'https://openalex.org/S50220091', 'display_name': 'Geometry & Topology', 'issn_l': '1364-0380', 'issn': ['1364-0380', '1465-3060'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, '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': 'bronze', 'oa_url': 'https://msp.org/gt/2010/14-4/gt-v14-n4-p10-s.pdf', 'any_repository_has_fulltext': True}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5079752528', 'display_name': 'Pierre‐Emmanuel Caprace', 'orcid': 'https://orcid.org/0000-0001-5294-2006'}, 'institutions': [{'id': 'https://openalex.org/I95674353', 'display_name': 'UCLouvain', 'ror': 'https://ror.org/02495e989', 'country_code': 'BE', 'type': 'education', 'lineage': ['https://openalex.org/I95674353']}], 'countries': ['BE'], 'is_corresponding': False, 'raw_author_name': 'Pierre-Emmanuel Caprace', 'raw_affiliation_strings': ['Département de Mathématiques, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium'], 'affiliations': [{'raw_affiliation_string': 'Département de Mathématiques, Université catholique de Louvain, Chemin du Cyclotron 2, 1348 Louvain-la-Neuve, Belgium', 'institution_ids': ['https://openalex.org/I95674353']}]}, {'author_position': 'last', 'author': {'id': 'https://openalex.org/A5002326870', 'display_name': 'Piotr Przytycki', 'orcid': 'https://orcid.org/0000-0002-4251-9383'}, 'institutions': [{'id': 'https://openalex.org/I99542240', 'display_name': 'Polish Academy of Sciences', 'ror': 'https://ror.org/01dr6c206', 'country_code': 'PL', 'type': 'government', 'lineage': ['https://openalex.org/I99542240']}, {'id': 'https://openalex.org/I4210137370', 'display_name': 'Institute of Mathematics', 'ror': 'https://ror.org/04hrrh248', 'country_code': 'PL', 'type': 'facility', 'lineage': ['https://openalex.org/I4210137370', 'https://openalex.org/I99542240']}], 'countries': ['PL'], 'is_corresponding': False, 'raw_author_name': 'Piotr Przytycki', 'raw_affiliation_strings': ['Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland'], 'affiliations': [{'raw_affiliation_string': 'Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warsaw, Poland', 'institution_ids': ['https://openalex.org/I99542240', 'https://openalex.org/I4210137370']}]}], 'institution_assertions': [], 'countries_distinct_count': 2, 'institutions_distinct_count': 3, 'corresponding_author_ids': [], 'corresponding_institution_ids': [], 'apc_list': None, 'apc_paid': None, 'fwci': 1.423, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 12, 'citation_normalized_percentile': {'value': 0.862394, 'is_in_top_1_percent': False, 'is_in_top_10_percent': False}, 'cited_by_percentile_year': {'min': 85, 'max': 86}, 'biblio': {'volume': '14', 'issue': '4', 'first_page': '2243', 'last_page': '2275'}, '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/T10304', 'display_name': 'Geometric and Algebraic Topology', '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/T10287', 'display_name': 'Algebraic structures and combinatorial models', 'score': 0.9966, '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/isomorphism', 'display_name': 'Isomorphism (crystallography)', 'score': 0.43519676}], 'concepts': [{'id': 'https://openalex.org/C143669375', 'wikidata': 'https://www.wikidata.org/wiki/Q7874246', 'display_name': 'Coxeter group', 'level': 2, 'score': 0.9844955}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.8201834}, {'id': 'https://openalex.org/C140860697', 'wikidata': 'https://www.wikidata.org/wiki/Q5179941', 'display_name': 'Coxeter element', 'level': 3, 'score': 0.7797753}, {'id': 'https://openalex.org/C201064014', 'wikidata': 'https://www.wikidata.org/wiki/Q3956993', 'display_name': 'Artin group', 'level': 3, 'score': 0.7789314}, {'id': 'https://openalex.org/C57796230', 'wikidata': 'https://www.wikidata.org/wiki/Q899720', 'display_name': 'Point group', 'level': 2, 'score': 0.7554996}, {'id': 'https://openalex.org/C37486056', 'wikidata': 'https://www.wikidata.org/wiki/Q5179939', 'display_name': 'Coxeter complex', 'level': 4, 'score': 0.6766495}, {'id': 'https://openalex.org/C48495023', 'wikidata': 'https://www.wikidata.org/wiki/Q6673739', 'display_name': 'Longest element of a Coxeter group', 'level': 5, 'score': 0.5294665}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.50855744}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.47542098}, {'id': 'https://openalex.org/C2776196297', 'wikidata': 'https://www.wikidata.org/wiki/Q17138781', 'display_name': 'Twist', 'level': 2, 'score': 0.45455965}, {'id': 'https://openalex.org/C203436722', 'wikidata': 'https://www.wikidata.org/wiki/Q902950', 'display_name': 'Isomorphism (crystallography)', 'level': 3, 'score': 0.43519676}, {'id': 'https://openalex.org/C16507315', 'wikidata': 'https://www.wikidata.org/wiki/Q7885104', 'display_name': 'Uniform k 21 polytope', 'level': 5, 'score': 0.4250642}, {'id': 'https://openalex.org/C2780990831', 'wikidata': 'https://www.wikidata.org/wiki/Q319141', 'display_name': 'Conjecture', 'level': 2, 'score': 0.42208236}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.09599364}, {'id': 'https://openalex.org/C49870271', 'wikidata': 'https://www.wikidata.org/wiki/Q193657', 'display_name': 'Convex set', 'level': 4, 'score': 0.0}, {'id': 'https://openalex.org/C157972887', 'wikidata': 'https://www.wikidata.org/wiki/Q463359', 'display_name': 'Convex optimization', 'level': 3, 'score': 0.0}, {'id': 'https://openalex.org/C112680207', 'wikidata': 'https://www.wikidata.org/wiki/Q714886', 'display_name': 'Regular polygon', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C115624301', 'wikidata': 'https://www.wikidata.org/wiki/Q895901', 'display_name': 'Crystal structure', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C185592680', 'wikidata': 'https://www.wikidata.org/wiki/Q2329', 'display_name': 'Chemistry', 'level': 0, 'score': 0.0}, {'id': 'https://openalex.org/C8010536', 'wikidata': 'https://www.wikidata.org/wiki/Q160398', 'display_name': 'Crystallography', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 5, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.2140/gt.2010.14.2243', 'pdf_url': 'https://msp.org/gt/2010/14-4/gt-v14-n4-p10-s.pdf', 'source': {'id': 'https://openalex.org/S50220091', 'display_name': 'Geometry & Topology', 'issn_l': '1364-0380', 'issn': ['1364-0380', '1465-3060'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, {'is_oa': True, 'landing_page_url': 'https://arxiv.org/abs/0911.0354', 'pdf_url': 'https://arxiv.org/pdf/0911.0354', '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/0911.0354.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://projecteuclid.org/euclid.gt/1513883518', 'pdf_url': 'https://projecteuclid.org/journals/geometry-and-topology/volume-14/issue-4/Twist-rigid-Coxeter-groups/10.2140/gt.2010.14.2243.pdf', 'source': {'id': 'https://openalex.org/S4306400787', 'display_name': 'Project Euclid (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.0911.0354', '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/10.2140/gt.2010.14.2243', 'pdf_url': 'https://msp.org/gt/2010/14-4/gt-v14-n4-p10-s.pdf', 'source': {'id': 'https://openalex.org/S50220091', 'display_name': 'Geometry & Topology', 'issn_l': '1364-0380', 'issn': ['1364-0380', '1465-3060'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310320446', 'host_organization_name': 'Mathematical Sciences Publishers', 'host_organization_lineage': ['https://openalex.org/P4310320446'], 'host_organization_lineage_names': ['Mathematical Sciences Publishers'], 'type': 'journal'}, 'license': None, 'license_id': None, 'version': 'publishedVersion', 'is_accepted': True, 'is_published': True}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': ['https://openalex.org/W2166469367', 'https://openalex.org/W3102260066'], 'referenced_works_count': 15, 'referenced_works': ['https://openalex.org/W1482318425', 'https://openalex.org/W1607402086', 'https://openalex.org/W1655530089', 'https://openalex.org/W1989477049', 'https://openalex.org/W1995010619', 'https://openalex.org/W2004730152', 'https://openalex.org/W2009820887', 'https://openalex.org/W2015227148', 'https://openalex.org/W2025803015', 'https://openalex.org/W2035856737', 'https://openalex.org/W2107839120', 'https://openalex.org/W2113867983', 'https://openalex.org/W2119974822', 'https://openalex.org/W3105974680', 'https://openalex.org/W633593841'], 'related_works': ['https://openalex.org/W4287272581', 'https://openalex.org/W3133786132', 'https://openalex.org/W3109211163', 'https://openalex.org/W3080202916', 'https://openalex.org/W2342132738', 'https://openalex.org/W2146451040', 'https://openalex.org/W2015422204', 'https://openalex.org/W1984460889', 'https://openalex.org/W1973786555', 'https://openalex.org/W1835158633'], 'abstract_inverted_index': {'We': [0], 'prove': [1], 'that': [2], 'two': [3], 'angle-compatible': [4], 'Coxeter': [5, 13, 46], 'generating': [6], 'sets': [7], 'of': [8, 19, 32], 'a': [9, 29, 33, 38], 'given': [10], 'finitely': [11], 'generated': [12], 'group': [14], 'are': [15], 'conjugate': [16], 'provided': [17], 'one': [18], 'them': [20], 'does': [21], 'not': [22], 'admit': [23], 'any': [24], 'elementary': [25], 'twist.': [26], 'This': [27], 'confirms': [28], 'basic': [30], 'case': [31], 'general': [34], 'conjecture': [35], 'which': [36], 'describes': [37], 'potential': [39], 'solution': [40], 'to': [41], 'the': [42], 'isomorphism': [43], 'problem': [44], 'for': [45], 'groups.': [47]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W2166469367', 'counts_by_year': [{'year': 2021, 'cited_by_count': 1}, {'year': 2018, 'cited_by_count': 2}, {'year': 2017, 'cited_by_count': 1}, {'year': 2016, 'cited_by_count': 1}, {'year': 2014, 'cited_by_count': 2}, {'year': 2013, 'cited_by_count': 2}], 'updated_date': '2024-12-08T20:35:19.431821', 'created_date': '2016-06-24'}