Get quick answers to your questions about the article from our AI researcher chatbot
{'id': 'https://openalex.org/W1495088152', 'doi': 'https://doi.org/10.1090/s0894-0347-05-00477-7', 'title': 'Enumerative tropical algebraic geometry in ℝ²', 'display_name': 'Enumerative tropical algebraic geometry in ℝ²', 'publication_year': 2005, 'publication_date': '2005-01-20', 'ids': {'openalex': 'https://openalex.org/W1495088152', 'doi': 'https://doi.org/10.1090/s0894-0347-05-00477-7', 'mag': '1495088152'}, 'language': 'en', 'primary_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/s0894-0347-05-00477-7', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S130224168', 'display_name': 'Journal of the American Mathematical Society', 'issn_l': '0894-0347', 'issn': ['0894-0347', '1088-6834'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, 'type': 'article', 'type_crossref': 'journal-article', 'indexed_in': ['crossref'], 'open_access': {'is_oa': True, 'oa_status': 'bronze', 'oa_url': 'https://doi.org/10.1090/s0894-0347-05-00477-7', 'any_repository_has_fulltext': False}, 'authorships': [{'author_position': 'first', 'author': {'id': 'https://openalex.org/A5087740280', 'display_name': 'Grigory Mikhalkin', 'orcid': 'https://orcid.org/0009-0008-9202-8938'}, 'institutions': [{'id': 'https://openalex.org/I84909340', 'display_name': 'Institut des Hautes Études Scientifiques', 'ror': 'https://ror.org/05d5m2r55', 'country_code': 'FR', 'type': 'facility', 'lineage': ['https://openalex.org/I84909340']}, {'id': 'https://openalex.org/I2801160905', 'display_name': 'Steklov Mathematical Institute', 'ror': 'https://ror.org/03zeg8w71', 'country_code': 'RU', 'type': 'facility', 'lineage': ['https://openalex.org/I1313323035', 'https://openalex.org/I2801160905', 'https://openalex.org/I4210124601']}, {'id': 'https://openalex.org/I185261750', 'display_name': 'University of Toronto', 'ror': 'https://ror.org/03dbr7087', 'country_code': 'CA', 'type': 'education', 'lineage': ['https://openalex.org/I185261750']}], 'countries': ['CA', 'FR', 'RU'], 'is_corresponding': True, 'raw_author_name': 'Grigory Mikhalkin', 'raw_affiliation_strings': ['Department of Mathematics, University of Toronto, 100 St. George St., Toronto, Ontario, M5S 3G3 Canada and St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191011 Russia', 'IHES, Le Bois-Marie, 35, route de Chartres, Bures-sur-Yvette, 91440, France'], 'affiliations': [{'raw_affiliation_string': 'IHES, Le Bois-Marie, 35, route de Chartres, Bures-sur-Yvette, 91440, France', 'institution_ids': ['https://openalex.org/I84909340']}, {'raw_affiliation_string': 'Department of Mathematics, University of Toronto, 100 St. George St., Toronto, Ontario, M5S 3G3 Canada and St. Petersburg Branch of Steklov Mathematical Institute, Fontanka 27, St. Petersburg, 191011 Russia', 'institution_ids': ['https://openalex.org/I2801160905', 'https://openalex.org/I185261750']}]}], 'institution_assertions': [], 'countries_distinct_count': 3, 'institutions_distinct_count': 3, 'corresponding_author_ids': ['https://openalex.org/A5087740280'], 'corresponding_institution_ids': ['https://openalex.org/I84909340', 'https://openalex.org/I2801160905', 'https://openalex.org/I185261750'], 'apc_list': None, 'apc_paid': None, 'fwci': 33.486, 'has_fulltext': True, 'fulltext_origin': 'pdf', 'cited_by_count': 619, 'citation_normalized_percentile': {'value': 0.999865, 'is_in_top_1_percent': True, 'is_in_top_10_percent': True}, 'cited_by_percentile_year': {'min': 99, 'max': 100}, 'biblio': {'volume': '18', 'issue': '2', 'first_page': '313', 'last_page': '377'}, 'is_retracted': False, 'is_paratext': False, 'primary_topic': {'id': 'https://openalex.org/T11435', 'display_name': 'Polynomial and algebraic computation', 'score': 0.9997, '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'}}, 'topics': [{'id': 'https://openalex.org/T11435', 'display_name': 'Polynomial and algebraic computation', 'score': 0.9997, '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': 0.9897, '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/T10061', 'display_name': 'Algebraic Geometry and Number Theory', 'score': 0.9862, '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/tropical-geometry', 'display_name': 'Tropical Geometry', 'score': 0.77441865}, {'id': 'https://openalex.org/keywords/polygon', 'display_name': 'Polygon (computer graphics)', 'score': 0.46585375}, {'id': 'https://openalex.org/keywords/newton-polygon', 'display_name': 'Newton polygon', 'score': 0.45774788}, {'id': 'https://openalex.org/keywords/lattice', 'display_name': 'Lattice (music)', 'score': 0.44478992}], 'concepts': [{'id': 'https://openalex.org/C202652594', 'wikidata': 'https://www.wikidata.org/wiki/Q2982669', 'display_name': 'Tropical geometry', 'level': 2, 'score': 0.77441865}, {'id': 'https://openalex.org/C33923547', 'wikidata': 'https://www.wikidata.org/wiki/Q395', 'display_name': 'Mathematics', 'level': 0, 'score': 0.7143462}, {'id': 'https://openalex.org/C204575570', 'wikidata': 'https://www.wikidata.org/wiki/Q207476', 'display_name': 'Holomorphic function', 'level': 2, 'score': 0.5571301}, {'id': 'https://openalex.org/C2524010', 'wikidata': 'https://www.wikidata.org/wiki/Q8087', 'display_name': 'Geometry', 'level': 1, 'score': 0.5222415}, {'id': 'https://openalex.org/C68363185', 'wikidata': 'https://www.wikidata.org/wiki/Q180969', 'display_name': 'Algebraic geometry', 'level': 2, 'score': 0.48342907}, {'id': 'https://openalex.org/C9376300', 'wikidata': 'https://www.wikidata.org/wiki/Q168817', 'display_name': 'Algebraic number', 'level': 2, 'score': 0.47676402}, {'id': 'https://openalex.org/C190694206', 'wikidata': 'https://www.wikidata.org/wiki/Q3276654', 'display_name': 'Polygon (computer graphics)', 'level': 3, 'score': 0.46585375}, {'id': 'https://openalex.org/C2777684946', 'wikidata': 'https://www.wikidata.org/wiki/Q115646', 'display_name': 'Newton polygon', 'level': 2, 'score': 0.45774788}, {'id': 'https://openalex.org/C207043602', 'wikidata': 'https://www.wikidata.org/wiki/Q266237', 'display_name': 'Algebraic curve', 'level': 2, 'score': 0.45389673}, {'id': 'https://openalex.org/C2781204021', 'wikidata': 'https://www.wikidata.org/wiki/Q6497091', 'display_name': 'Lattice (music)', 'level': 2, 'score': 0.44478992}, {'id': 'https://openalex.org/C114614502', 'wikidata': 'https://www.wikidata.org/wiki/Q76592', 'display_name': 'Combinatorics', 'level': 1, 'score': 0.37985274}, {'id': 'https://openalex.org/C11413529', 'wikidata': 'https://www.wikidata.org/wiki/Q8366', 'display_name': 'Algorithm', 'level': 1, 'score': 0.37302232}, {'id': 'https://openalex.org/C136119220', 'wikidata': 'https://www.wikidata.org/wiki/Q1000660', 'display_name': 'Algebra over a field', 'level': 2, 'score': 0.33054632}, {'id': 'https://openalex.org/C118615104', 'wikidata': 'https://www.wikidata.org/wiki/Q121416', 'display_name': 'Discrete mathematics', 'level': 1, 'score': 0.23482728}, {'id': 'https://openalex.org/C202444582', 'wikidata': 'https://www.wikidata.org/wiki/Q837863', 'display_name': 'Pure mathematics', 'level': 1, 'score': 0.22522819}, {'id': 'https://openalex.org/C134306372', 'wikidata': 'https://www.wikidata.org/wiki/Q7754', 'display_name': 'Mathematical analysis', 'level': 1, 'score': 0.1515547}, {'id': 'https://openalex.org/C41008148', 'wikidata': 'https://www.wikidata.org/wiki/Q21198', 'display_name': 'Computer science', 'level': 0, 'score': 0.14553824}, {'id': 'https://openalex.org/C121332964', 'wikidata': 'https://www.wikidata.org/wiki/Q413', 'display_name': 'Physics', 'level': 0, 'score': 0.06795749}, {'id': 'https://openalex.org/C76155785', 'wikidata': 'https://www.wikidata.org/wiki/Q418', 'display_name': 'Telecommunications', 'level': 1, 'score': 0.0}, {'id': 'https://openalex.org/C126042441', 'wikidata': 'https://www.wikidata.org/wiki/Q1324888', 'display_name': 'Frame (networking)', 'level': 2, 'score': 0.0}, {'id': 'https://openalex.org/C24890656', 'wikidata': 'https://www.wikidata.org/wiki/Q82811', 'display_name': 'Acoustics', 'level': 1, 'score': 0.0}], 'mesh': [], 'locations_count': 1, 'locations': [{'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/s0894-0347-05-00477-7', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S130224168', 'display_name': 'Journal of the American Mathematical Society', 'issn_l': '0894-0347', 'issn': ['0894-0347', '1088-6834'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}], 'best_oa_location': {'is_oa': True, 'landing_page_url': 'https://doi.org/10.1090/s0894-0347-05-00477-7', 'pdf_url': None, 'source': {'id': 'https://openalex.org/S130224168', 'display_name': 'Journal of the American Mathematical Society', 'issn_l': '0894-0347', 'issn': ['0894-0347', '1088-6834'], 'is_oa': False, 'is_in_doaj': False, 'is_core': True, 'host_organization': 'https://openalex.org/P4310315719', 'host_organization_name': 'American Mathematical Society', 'host_organization_lineage': ['https://openalex.org/P4310315719'], 'host_organization_lineage_names': ['American Mathematical Society'], 'type': 'journal'}, 'license': 'publisher-specific-oa', 'license_id': 'https://openalex.org/licenses/publisher-specific-oa', 'version': 'acceptedVersion', 'is_accepted': True, 'is_published': False}, 'sustainable_development_goals': [], 'grants': [], 'datasets': [], 'versions': [], 'referenced_works_count': 34, 'referenced_works': ['https://openalex.org/W1609080720', 'https://openalex.org/W1634361432', 'https://openalex.org/W1771655831', 'https://openalex.org/W1977415556', 'https://openalex.org/W1978714019', 'https://openalex.org/W1999235582', 'https://openalex.org/W2004791166', 'https://openalex.org/W2021591064', 'https://openalex.org/W2032380679', 'https://openalex.org/W2033437043', 'https://openalex.org/W2039970970', 'https://openalex.org/W2041883807', 'https://openalex.org/W2044681045', 'https://openalex.org/W2055287661', 'https://openalex.org/W2056254807', 'https://openalex.org/W2070765658', 'https://openalex.org/W2079988604', 'https://openalex.org/W2094372703', 'https://openalex.org/W2098960371', 'https://openalex.org/W2100363938', 'https://openalex.org/W2112968295', 'https://openalex.org/W2140948062', 'https://openalex.org/W2160740909', 'https://openalex.org/W217710249', 'https://openalex.org/W2579365473', 'https://openalex.org/W2792841820', 'https://openalex.org/W2951199322', 'https://openalex.org/W3037199498', 'https://openalex.org/W3039948875', 'https://openalex.org/W3099597568', 'https://openalex.org/W3100385724', 'https://openalex.org/W3103324632', 'https://openalex.org/W582672715', 'https://openalex.org/W85883491'], 'related_works': ['https://openalex.org/W85922473', 'https://openalex.org/W4251745762', 'https://openalex.org/W321614567', 'https://openalex.org/W3198902617', 'https://openalex.org/W3094170991', 'https://openalex.org/W3042074040', 'https://openalex.org/W2804118840', 'https://openalex.org/W2734824228', 'https://openalex.org/W2614394667', 'https://openalex.org/W2259933724'], 'abstract_inverted_index': {'The': [0, 34, 58], 'paper': [1], 'establishes': [2], 'a': [3], 'formula': [4, 35], 'for': [5], 'enumeration': [6], 'of': [7, 9, 26, 65], 'curves': [8, 20, 41, 110], 'arbitrary': [10], 'genus': [11], 'in': [12, 30, 39, 45], 'toric': [13, 78], 'surfaces.': [14], 'It': [15], 'turns': [16], 'out': [17], 'that': [18], 'such': [19], 'can': [21], 'be': [22], 'counted': [23], 'by': [24], 'means': [25], 'certain': [27, 112], 'lattice': [28, 43], 'paths': [29, 44], 'the': [31, 63, 66, 81], 'Newton': [32], 'polygon.': [33], 'was': [36], 'announced': [37], 'earlier': [38], '<italic>Counting': [40], 'via': [42], 'polygons,</italic>': [46], 'C.': [47], 'R.': [48], 'Math.': [49], 'Acad.': [50], 'Sci.': [51], 'Paris': [52], '<bold>336</bold>': [53], '(2003),': [54], 'no.': [55], '8,': [56], '629–634.': [57], 'result': [59], 'is': [60], 'established': [61], 'with': [62, 80, 111], 'help': [64], 'so-called': [67], 'tropical': [68], 'algebraic': [69], 'geometry.': [70], 'This': [71], 'geometry': [72], 'allows': [73], 'one': [74], 'to': [75], 'replace': [76], 'complex': [77], 'varieties': [79], 'real': [82], 'space': [83], '<inline-formula': [84], 'content-type="math/mathml">': [85], '<mml:math': [86], 'xmlns:mml="http://www.w3.org/1998/Math/MathML"': [87], 'alttext="double-struck': [88], 'upper': [89], 'R': [90], 'Superscript': [91], 'n">': [92], '<mml:semantics>': [93], '<mml:msup>': [94], '<mml:mrow': [95], 'class="MJX-TeXAtom-ORD">': [96], '<mml:mi': [97], 'mathvariant="double-struck">R</mml:mi>': [98], '</mml:mrow>': [99], '<mml:mi>n</mml:mi>': [100], '</mml:msup>': [101], '<mml:annotation': [102], 'encoding="application/x-tex">\\mathbb': [103], '{R}^n</mml:annotation>': [104], '</mml:semantics>': [105], '</mml:math>': [106], '</inline-formula>': [107], 'and': [108], 'holomorphic': [109], 'piecewise-linear': [113], 'graphs': [114], 'there.': [115]}, 'cited_by_api_url': 'https://api.openalex.org/works?filter=cites:W1495088152', 'counts_by_year': [{'year': 2024, 'cited_by_count': 20}, {'year': 2023, 'cited_by_count': 20}, {'year': 2022, 'cited_by_count': 28}, {'year': 2021, 'cited_by_count': 30}, {'year': 2020, 'cited_by_count': 34}, {'year': 2019, 'cited_by_count': 35}, {'year': 2018, 'cited_by_count': 33}, {'year': 2017, 'cited_by_count': 29}, {'year': 2016, 'cited_by_count': 34}, {'year': 2015, 'cited_by_count': 44}, {'year': 2014, 'cited_by_count': 34}, {'year': 2013, 'cited_by_count': 27}, {'year': 2012, 'cited_by_count': 26}], 'updated_date': '2024-12-18T20:06:18.315988', 'created_date': '2016-06-24'}