{"id":"https://openalex.org/W2993394850","doi":"https://doi.org/10.37236/1637","title":"Exchange Symmetries in Motzkin Path and Bargraph Models of Copolymer Adsorption","display_name":"Exchange Symmetries in Motzkin Path and Bargraph Models of Copolymer Adsorption","publication_year":2002,"publication_date":"2002-04-23","ids":{"openalex":"https://openalex.org/W2993394850","doi":"https://doi.org/10.37236/1637","mag":"2993394850"},"language":"en","primary_location":{"id":"doi:10.37236/1637","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1637","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r20/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052790968","display_name":"E J Janse van Rensburg","orcid":"https://orcid.org/0000-0003-4366-634X"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"E. J. Janse van Rensburg","raw_affiliation_strings":["Department of Mathematics and Statistics York University, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics York University, Ontario, Canada","institution_ids":["https://openalex.org/I192455969"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043988338","display_name":"Andrew Rechnitzer","orcid":"https://orcid.org/0000-0002-4386-3207"},"institutions":[{"id":"https://openalex.org/I192455969","display_name":"York University","ror":"https://ror.org/05fq50484","country_code":"CA","type":"education","lineage":["https://openalex.org/I192455969"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"A. Rechnitzer","raw_affiliation_strings":["Department of Mathematics and Statistics York University, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics York University, Ontario, Canada","institution_ids":["https://openalex.org/I192455969"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043988338"],"corresponding_institution_ids":["https://openalex.org/I192455969"],"apc_list":null,"apc_paid":null,"fwci":1.1677,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.78062058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"9","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":0.9988999962806702,"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":0.9988999962806702,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.7402891516685486},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6566122174263},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6455380916595459},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5232964158058167},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5010132789611816},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.45490700006484985},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.4212993085384369},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2742987871170044},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11164459586143494},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08836591243743896}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7402891516685486},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6566122174263},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6455380916595459},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5232964158058167},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5010132789611816},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.45490700006484985},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.4212993085384369},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2742987871170044},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11164459586143494},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08836591243743896},{"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:10.37236/1637","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1637","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r20/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.4.8535","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.4.8535","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PostScriptfiles/v9i1r20.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.5.2882","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.5.2882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_9/PDF/v9i1r20.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1637","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1637","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r20/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":false,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2165548363","display_name":null,"funder_award_id":"Canada","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2993394850.pdf","grobid_xml":"https://content.openalex.org/works/W2993394850.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W286262720","https://openalex.org/W596157542","https://openalex.org/W1504241636","https://openalex.org/W1577336286","https://openalex.org/W1970922629","https://openalex.org/W1973028181","https://openalex.org/W1977379849","https://openalex.org/W1980486012","https://openalex.org/W1987511152","https://openalex.org/W2004056472","https://openalex.org/W2004585164","https://openalex.org/W2010100934","https://openalex.org/W2011626174","https://openalex.org/W2011984492","https://openalex.org/W2013329409","https://openalex.org/W2019466795","https://openalex.org/W2025773144","https://openalex.org/W2028750928","https://openalex.org/W2034892484","https://openalex.org/W2035683171","https://openalex.org/W2036252950","https://openalex.org/W2047219397","https://openalex.org/W2053177808","https://openalex.org/W2079699338","https://openalex.org/W2089554292","https://openalex.org/W2089624392","https://openalex.org/W2115059819","https://openalex.org/W3104467049","https://openalex.org/W4300302225","https://openalex.org/W4388317767"],"related_works":["https://openalex.org/W4300711749","https://openalex.org/W2246967737","https://openalex.org/W2080482296","https://openalex.org/W2950842770","https://openalex.org/W136698236","https://openalex.org/W3186968207","https://openalex.org/W1973655965","https://openalex.org/W2008488552","https://openalex.org/W3016004364","https://openalex.org/W2141420903"],"abstract_inverted_index":{"In":[0,98,199],"a":[1,22,35,65,73,93],"previous":[2,124],"work":[3],"[26],":[4],"by":[5],"considering":[6],"paths":[7,17],"that":[8],"are":[9,119,142],"partially":[10,106,167,179],"weighted,":[11],"the":[12,32,38,53,85,90,96,111,127,133,136,139,149,154,166,186,189,209,217,221],"generating":[13,54,210],"function":[14,94],"of":[15,24,34,37,56,59,68,89,95,110,123,131,138,188,191],"Dyck":[16,61],"was":[18],"shown":[19],"to":[20,79,144,183,215],"possess":[21],"type":[23],"symmetry,":[25],"called":[26],"an":[27,81,120,196],"exchange":[28,33,206],"relation,":[29],"derived":[30],"from":[31],"portion":[36],"path":[39,104,156],"between":[40],"weighted":[41],"and":[42,71,105,161,164,194,212],"unweighted":[43],"halves.":[44],"This":[45],"relation":[46],"is":[47,64,77],"particularly":[48],"useful":[49],"in":[50,72,153,178],"solving":[51],"for":[52,84,148,158,165,171,208,220],"functions":[55],"certain":[57],"models":[58,109],"vertex-coloured":[60],"paths;":[62],"this":[63,99,192],"directed":[66,107,114,168,180],"model":[67,91,157],"copolymer":[69,115],"adsorption,":[70],"particular":[74],"case":[75],"it":[76],"possible":[78],"find":[80,145,205,216],"asymptotic":[82,146,218],"expression":[83,219],"adsorption":[86,150,222],"critical":[87,151,223],"point":[88,152],"as":[92],"colouring.":[97],"paper":[100],"we":[101,203],"examine":[102],"Motzkin":[103,155],"walk":[108,169],"same":[112],"adsorbing":[113],"problem.":[116],"These":[117],"problems":[118],"interesting":[121],"generalisation":[122],"results":[125],"since":[126],"colouring":[128,176],"can":[129],"be":[130,184],"either":[132],"edges,":[134],"or":[135],"vertices,":[137],"paths.":[140],"We":[141],"able":[143],"expressions":[147],"both":[159,200],"edge":[160,172],"vertex":[162,175],"colourings,":[163],"only":[170],"colourings.":[173],"The":[174],"problem":[177],"walks":[181],"seems":[182],"beyond":[185],"scope":[187],"methods":[190],"paper,":[193],"remains":[195],"open":[197],"question.":[198],"these":[201],"cases":[202],"first":[204],"relations":[207],"functions,":[211],"use":[213],"those":[214],"point.":[224]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":24},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}