{"id":"https://openalex.org/W2998875174","doi":"https://doi.org/10.1137/20m1370975","title":"Faces of Root Polytopes","display_name":"Faces of Root Polytopes","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2998875174","doi":"https://doi.org/10.1137/20m1370975","mag":"2998875174"},"language":"en","primary_location":{"id":"doi:10.1137/20m1370975","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1370975","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.05191","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071855262","display_name":"Linus Setiabrata","orcid":"https://orcid.org/0000-0001-6725-2518"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Linus Setiabrata","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5071855262"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05383412,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"3","first_page":"2093","last_page":"2114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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":0.9998000264167786,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9865000247955322,"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":0.936525821685791},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6991192102432251},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.6981194615364075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5428833961486816},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5008056163787842},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.09264364838600159},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.07952940464019775},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.0676773190498352}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.936525821685791},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6991192102432251},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.6981194615364075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5428833961486816},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5008056163787842},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.09264364838600159},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07952940464019775},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0676773190498352}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1370975","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1370975","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2001.05191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.05191","pdf_url":"https://arxiv.org/pdf/2001.05191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2998875174","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.05191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2001.05191","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2001.05191","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2001.05191","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2001.05191","pdf_url":"https://arxiv.org/pdf/2001.05191","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1556866066","https://openalex.org/W1597196612","https://openalex.org/W1658553078","https://openalex.org/W1949656854","https://openalex.org/W2054374453","https://openalex.org/W2063740845","https://openalex.org/W2090824304","https://openalex.org/W2105527809","https://openalex.org/W2119507535","https://openalex.org/W2130848020","https://openalex.org/W2488594862","https://openalex.org/W2789282835","https://openalex.org/W2964131157","https://openalex.org/W3090997489","https://openalex.org/W4248855403"],"related_works":["https://openalex.org/W3199929324","https://openalex.org/W1489911386","https://openalex.org/W2950120006","https://openalex.org/W2148642357","https://openalex.org/W2038021690","https://openalex.org/W2019529322","https://openalex.org/W2058724874","https://openalex.org/W1923369141","https://openalex.org/W2332275131","https://openalex.org/W2887434114","https://openalex.org/W1879658246","https://openalex.org/W2033234590","https://openalex.org/W1990980885","https://openalex.org/W2951611396","https://openalex.org/W2951487779","https://openalex.org/W1679454549","https://openalex.org/W2055018987","https://openalex.org/W3204693605","https://openalex.org/W2949890362","https://openalex.org/W2086660719"],"abstract_inverted_index":{"We":[0],"completely":[1],"characterize":[2],"the":[3,6,29],"faces":[4],"of":[5,28],"root":[7],"polytope":[8],"$\\tilde":[9],"Q_G":[10],"=":[11],"\\text{conv}\\{\\mathbf":[12],"0,":[13],"\\mathbf":[14,17],"e_i":[15],"-":[16],"e_j\\:":[18],"(i,j)":[19],"\\in":[20],"E(G)\\}$":[21],"combinatorially.":[22],"Our":[23],"results":[24,31],"specialize":[25],"to":[26],"state":[27],"art":[30],"in":[32],"a":[33],"straightforward":[34],"way.":[35]},"counts_by_year":[],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}