{"id":"https://openalex.org/W4225771993","doi":"https://doi.org/10.37236/10913","title":"An Extension of the Lindstr\u00f6m-Gessel-Viennot Theorem","display_name":"An Extension of the Lindstr\u00f6m-Gessel-Viennot Theorem","publication_year":2022,"publication_date":"2022-06-03","ids":{"openalex":"https://openalex.org/W4225771993","doi":"https://doi.org/10.37236/10913"},"language":"en","primary_location":{"id":"doi:10.37236/10913","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10913","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p41/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/v29i2p41/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039669216","display_name":"Yi-Lin Lee","orcid":"https://orcid.org/0000-0002-7200-4735"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yi-Lin Lee","raw_affiliation_strings":["Indiana University at Bloomington"],"affiliations":[{"raw_affiliation_string":"Indiana University at Bloomington","institution_ids":["https://openalex.org/I4210119109"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5039669216"],"corresponding_institution_ids":["https://openalex.org/I4210119109"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.14207275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"2","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":0.9983000159263611,"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":0.9983000159263611,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9807999730110168,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.8714557886123657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7310105562210083},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7011240720748901},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6068784594535828},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5177663564682007},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.4898638427257538},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4810781180858612},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.43936580419540405},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3787153363227844},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1300276815891266},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0900004506111145},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0855419933795929}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8714557886123657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7310105562210083},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7011240720748901},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6068784594535828},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5177663564682007},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.4898638427257538},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4810781180858612},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.43936580419540405},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3787153363227844},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1300276815891266},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0900004506111145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0855419933795929},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/10913","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10913","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p41/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:2112.06115","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2112.06115","pdf_url":"https://arxiv.org/pdf/2112.06115","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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2112.06115","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2112.06115","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-journal"}],"best_oa_location":{"id":"doi:10.37236/10913","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10913","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p41/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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4225771993.pdf","grobid_xml":"https://content.openalex.org/works/W4225771993.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1513031742","https://openalex.org/W1709126960","https://openalex.org/W1746987937","https://openalex.org/W1795604484","https://openalex.org/W1826468728","https://openalex.org/W1967472879","https://openalex.org/W1977628371","https://openalex.org/W2091216084","https://openalex.org/W2102664288","https://openalex.org/W2106962889","https://openalex.org/W2417347603","https://openalex.org/W6622003828"],"related_works":["https://openalex.org/W80754151","https://openalex.org/W18935875","https://openalex.org/W49648587","https://openalex.org/W67803472","https://openalex.org/W31673381","https://openalex.org/W44584675","https://openalex.org/W7780232","https://openalex.org/W32909916","https://openalex.org/W46648024","https://openalex.org/W73159664"],"abstract_inverted_index":{"Consider":[0],"a":[1,14,60],"weighted":[2],"directed":[3],"acyclic":[4],"graph":[5],"$G$":[6,27],"having":[7],"an":[8],"upward":[9],"planar":[10],"drawing.":[11],"We":[12],"give":[13],"formula":[15],"for":[16],"the":[17,21,36,40,48,54],"total":[18],"weight":[19],"of":[20,23,43,67],"families":[22],"non-intersecting":[24],"paths":[25,69],"on":[26],"with":[28,70],"any":[29],"given":[30,71],"starting":[31,72],"and":[32,73],"ending":[33,74],"points.":[34,75],"While":[35],"Lindstr\u00f6m-Gessel-Viennot":[37],"theorem":[38],"gives":[39],"signed":[41,65],"enumeration":[42],"these":[44],"weights":[45],"(according":[46],"to":[47],"connection":[49],"type),":[50],"our":[51],"result":[52],"provides":[53],"straight":[55],"count,":[56],"expressing":[57],"it":[58],"as":[59],"determinant":[61],"whose":[62],"entries":[63],"are":[64],"counts":[66],"lattice":[68]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2022-05-05T00:00:00"}