{"id":"https://openalex.org/W2750826767","doi":"https://doi.org/10.37236/8256","title":"The Rank Function of a Positroid and Non-Crossing Partitions","display_name":"The Rank Function of a Positroid and Non-Crossing Partitions","publication_year":2020,"publication_date":"2020-01-10","ids":{"openalex":"https://openalex.org/W2750826767","doi":"https://doi.org/10.37236/8256","mag":"2750826767"},"language":"en","primary_location":{"id":"doi:10.37236/8256","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8256","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p11/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025903130","display_name":"Robert Mcalmon","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Mcalmon","raw_affiliation_strings":["Texas State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076585095","display_name":"Suho Oh","orcid":"https://orcid.org/0000-0002-4856-9197"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suho Oh","raw_affiliation_strings":["Texas State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Texas State University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01414949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9986000061035156,"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":0.9986000061035156,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9865000247955322,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8617289066314697},{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.8252390027046204},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7921178936958313},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.7896530032157898},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7419947385787964},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.71126389503479},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6717051267623901},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.523101806640625},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.5043100118637085},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4600183367729187},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09783884882926941}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8617289066314697},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.8252390027046204},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7921178936958313},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.7896530032157898},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7419947385787964},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.71126389503479},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6717051267623901},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.523101806640625},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.5043100118637085},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4600183367729187},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09783884882926941},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8256","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8256","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1709.01580","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.01580","pdf_url":"https://arxiv.org/pdf/1709.01580","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:2750826767","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1709.01580.pdf","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.1709.01580","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1709.01580","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":"doi:10.37236/8256","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8256","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i1p11/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2750826767.pdf"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1672638072","https://openalex.org/W1717558315","https://openalex.org/W1931704346","https://openalex.org/W2054663063","https://openalex.org/W2090366362","https://openalex.org/W2136499036","https://openalex.org/W2148858993","https://openalex.org/W2473957746","https://openalex.org/W2794984779","https://openalex.org/W2964272847","https://openalex.org/W6640250967"],"related_works":["https://openalex.org/W2999324977","https://openalex.org/W2585863988","https://openalex.org/W1931704346","https://openalex.org/W2733537833","https://openalex.org/W2963030844","https://openalex.org/W3153765276","https://openalex.org/W2890415486","https://openalex.org/W2460174513","https://openalex.org/W2346625941","https://openalex.org/W2118478818","https://openalex.org/W2993985424","https://openalex.org/W2023927275","https://openalex.org/W3082603173","https://openalex.org/W2050035633","https://openalex.org/W2768309459","https://openalex.org/W2951173598","https://openalex.org/W2047749352","https://openalex.org/W2006159741","https://openalex.org/W3110299859","https://openalex.org/W2952429652"],"abstract_inverted_index":{"A":[0],"positroid":[1,49,77],"is":[2],"a":[3,7,48,76],"special":[4],"case":[5],"of":[6,15,19,35,47,56,71],"realizable":[8],"matroid,":[9],"that":[10,26,68],"arose":[11],"from":[12,82],"the":[13,20,57,69,83],"study":[14],"totally":[16],"nonnegative":[17],"part":[18],"Grassmannian":[21],"by":[22],"Postnikov.":[23],"Postnikov":[24],"demonstrated":[25],"positroids":[27],"are":[28],"in":[29,54,75],"bijection":[30],"with":[31],"certain":[32],"interesting":[33],"classes":[34],"combinatorial":[36],"objects,":[37],"such":[38],"as":[39],"Grassmann":[40,58],"necklaces":[41],"and":[42,60],"decorated":[43,61,85],"permutations.":[44],"The":[45],"bases":[46],"can":[50,78],"be":[51,79],"described":[52],"directly":[53,81],"terms":[55],"necklace":[59],"permutation.":[62],"In":[63],"this":[64],"paper,":[65],"we":[66],"show":[67],"rank":[70],"an":[72],"arbitrary":[73],"set":[74],"computed":[80],"associated":[84],"permutation":[86],"using":[87],"non-crossing":[88],"partitions.":[89]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}