{"id":"https://openalex.org/W2006093530","doi":"https://doi.org/10.1007/s00454-006-1294-3","title":"Alcoved Polytopes, I","display_name":"Alcoved Polytopes, I","publication_year":2007,"publication_date":"2007-10-01","ids":{"openalex":"https://openalex.org/W2006093530","doi":"https://doi.org/10.1007/s00454-006-1294-3","mag":"2006093530"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-006-1294-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-006-1294-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1294-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1294-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079339565","display_name":"Thomas Lam","orcid":"https://orcid.org/0000-0003-2346-7685"},"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":"Thomas Lam","raw_affiliation_strings":["Department of Mathematics, M.I.T., Cambridge, MA 02139, USA","Department of Mathematics, M.I.T, Cambridge, MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, M.I.T., Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics, M.I.T, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110617923","display_name":"Alexander Postnikov","orcid":null},"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":false,"raw_author_name":"Alexander Postnikov","raw_affiliation_strings":["Department of Mathematics, M.I.T., Cambridge, MA 02139, USA","Department of Mathematics, M.I.T, Cambridge, MA 02139, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, M.I.T., Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics, M.I.T, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079339565"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.8175,"has_fulltext":true,"cited_by_count":105,"citation_normalized_percentile":{"value":0.94524496,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"38","issue":"3","first_page":"453","last_page":"478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":1.0,"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":1.0,"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":"Algebraic structures and combinatorial models","score":0.9939000010490417,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9929999709129333,"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/polytope","display_name":"Polytope","score":0.9520338773727417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8349480032920837},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.7144562602043152},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6891536116600037},{"id":"https://openalex.org/keywords/coxeter-group","display_name":"Coxeter group","score":0.5931881666183472},{"id":"https://openalex.org/keywords/polytope-model","display_name":"Polytope model","score":0.5893549919128418},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.532157301902771},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5215132832527161},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.4949449896812439},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.47632843255996704},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.4586077332496643},{"id":"https://openalex.org/keywords/polyhedral-combinatorics","display_name":"Polyhedral combinatorics","score":0.41781026124954224},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15024515986442566},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11328011751174927},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.08582803606987},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08533430099487305},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.0699022114276886}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9520338773727417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8349480032920837},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.7144562602043152},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6891536116600037},{"id":"https://openalex.org/C143669375","wikidata":"https://www.wikidata.org/wiki/Q7874246","display_name":"Coxeter group","level":2,"score":0.5931881666183472},{"id":"https://openalex.org/C113391598","wikidata":"https://www.wikidata.org/wiki/Q1681391","display_name":"Polytope model","level":3,"score":0.5893549919128418},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.532157301902771},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5215132832527161},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.4949449896812439},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.47632843255996704},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.4586077332496643},{"id":"https://openalex.org/C174248988","wikidata":"https://www.wikidata.org/wiki/Q8348314","display_name":"Polyhedral combinatorics","level":5,"score":0.41781026124954224},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15024515986442566},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11328011751174927},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.08582803606987},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08533430099487305},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.0699022114276886},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00454-006-1294-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-006-1294-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1294-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.134.174","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.174","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.mit.edu/~apost/papers/alcoved1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.236.3431","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.236.3431","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0501246v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.237.688","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.237.688","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0501246v2.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-006-1294-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-006-1294-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-006-1294-3.pdf","source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5199999809265137}],"awards":[{"id":"https://openalex.org/G4783094762","display_name":"Algebraic Combinatorics and its Applications","funder_award_id":"0201494","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2006093530.pdf","grobid_xml":"https://content.openalex.org/works/W2006093530.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W161168904","https://openalex.org/W596713504","https://openalex.org/W1521877949","https://openalex.org/W1593866140","https://openalex.org/W1608151808","https://openalex.org/W1972777548","https://openalex.org/W1979423085","https://openalex.org/W2009190506","https://openalex.org/W2015676663","https://openalex.org/W2021636827","https://openalex.org/W2033172904","https://openalex.org/W2057459399","https://openalex.org/W2064031190","https://openalex.org/W2117707498","https://openalex.org/W3088734221","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W34983847","https://openalex.org/W2952140350","https://openalex.org/W2181847787","https://openalex.org/W2950719732","https://openalex.org/W2922236301","https://openalex.org/W4288417334","https://openalex.org/W2164572645","https://openalex.org/W1989517190","https://openalex.org/W4387695124","https://openalex.org/W2016944804"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":11},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}