{"id":"https://openalex.org/W2962750824","doi":"https://doi.org/10.37236/7055","title":"Orbits of Antichains in Certain Root Posets","display_name":"Orbits of Antichains in Certain Root Posets","publication_year":2017,"publication_date":"2017-10-20","ids":{"openalex":"https://openalex.org/W2962750824","doi":"https://doi.org/10.37236/7055","mag":"2962750824"},"language":"en","primary_location":{"id":"doi:10.37236/7055","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7055","pdf_url":null,"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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/7055","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113901879","display_name":"Chao-Ping Dong","orcid":null},"institutions":[{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CN","CZ"],"is_corresponding":true,"raw_author_name":"Chao-Ping Dong","raw_affiliation_strings":["Institute of Mathematics,  Hunan University"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics,  Hunan University","institution_ids":["https://openalex.org/I16609230","https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030556566","display_name":"Suijie Wang","orcid":"https://orcid.org/0000-0001-6854-5611"},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BG","CN","CZ"],"is_corresponding":false,"raw_author_name":"Suijie Wang","raw_affiliation_strings":["Institute of Mathematics,  Hunan University"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics,  Hunan University","institution_ids":["https://openalex.org/I16609230","https://openalex.org/I4210105926","https://openalex.org/I4210120266"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5113901879"],"corresponding_institution_ids":["https://openalex.org/I16609230","https://openalex.org/I4210105926","https://openalex.org/I4210120266"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.2970964,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.993399977684021,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.993399977684021,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9898999929428101,"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"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.984499990940094,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/partially-ordered-set","display_name":"Partially ordered set","score":0.885019838809967},{"id":"https://openalex.org/keywords/antichain","display_name":"Antichain","score":0.8066222667694092},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7389165759086609},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7277011275291443},{"id":"https://openalex.org/keywords/orbit","display_name":"Orbit (dynamics)","score":0.5456727743148804},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5326658487319946},{"id":"https://openalex.org/keywords/root","display_name":"Root (linguistics)","score":0.5287520289421082},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3396648168563843},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05533131957054138},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.05351513624191284}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.885019838809967},{"id":"https://openalex.org/C136134351","wikidata":"https://www.wikidata.org/wiki/Q431937","display_name":"Antichain","level":3,"score":0.8066222667694092},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7389165759086609},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7277011275291443},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.5456727743148804},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5326658487319946},{"id":"https://openalex.org/C171078966","wikidata":"https://www.wikidata.org/wiki/Q111029","display_name":"Root (linguistics)","level":2,"score":0.5287520289421082},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3396648168563843},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05533131957054138},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.05351513624191284},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7055","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7055","pdf_url":null,"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"}],"best_oa_location":{"id":"doi:10.37236/7055","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7055","pdf_url":null,"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":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2013313833","https://openalex.org/W28336341","https://openalex.org/W2111205855","https://openalex.org/W2015816871","https://openalex.org/W1854642140","https://openalex.org/W2056881277","https://openalex.org/W2065333210","https://openalex.org/W1504624230","https://openalex.org/W3213974985","https://openalex.org/W4302107529"],"abstract_inverted_index":{"Building":[0],"everything":[1],"from":[2],"scratch,":[3],"we":[4,45],"give":[5],"another":[6],"proof":[7],"of":[8,24,51,58,87],"Propp":[9,108],"and":[10,79,109],"Roby's":[11],"theorem":[12],"saying":[13],"that":[14,34,47,76],"the":[15,25,48,66,103],"average":[16,49],"antichain":[17],"size":[18,50],"in":[19,53],"any":[20,54],"reverse":[21,55],"operator":[22,56],"orbit":[23,57],"poset":[26,68],"$[m]\\times":[27,59,77,80],"[n]$":[28,78],"is":[29,32,65],"$\\frac{mn}{m+n}$.":[30],"It":[31],"conceivable":[33],"our":[35],"method":[36],"should":[37,96],"work":[38],"for":[39],"other":[40],"situations.":[41],"As":[42],"a":[43,98],"demonstration,":[44],"show":[46],"antichains":[52],"K_{n-1}$":[60,81],"equals":[61],"$\\frac{2mn}{m+2n-1}$.":[62],"Here":[63],"$K_{n-1}$":[64],"minuscule":[67],"$[n-1]\\oplus":[69],"([1]":[70],"\\sqcup":[71],"[1])":[72],"\\oplus":[73],"[n-1]$.":[74],"Note":[75],"can":[82],"be":[83],"interpreted":[84],"as":[85],"sub-families":[86],"certain":[88],"root":[89,94],"posets.":[90],"We":[91],"guess":[92],"these":[93],"posets":[95],"provide":[97],"unified":[99],"setting":[100],"to":[101],"exhibit":[102],"homomesy":[104],"phenomenon":[105],"defined":[106],"by":[107],"Roby.":[110]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}