{"id":"https://openalex.org/W2999505892","doi":"https://doi.org/10.37236/1971","title":"Chain Polynomials of Distributive Lattices are 75% Unimodal","display_name":"Chain Polynomials of Distributive Lattices are 75% Unimodal","publication_year":2005,"publication_date":"2005-03-14","ids":{"openalex":"https://openalex.org/W2999505892","doi":"https://doi.org/10.37236/1971","mag":"2999505892"},"language":"en","primary_location":{"id":"doi:10.37236/1971","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1971","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n4/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":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":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n4/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024148075","display_name":"Anders Bj\u00f6rner","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Anders Bj\u00f6rner","raw_affiliation_strings":["Department of Mathematics Royal Institute of Technology S-100 44 Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Royal Institute of Technology S-100 44 Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062949530","display_name":"Jonathan David Farley","orcid":"https://orcid.org/0000-0003-3247-6014"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jonathan David Farley","raw_affiliation_strings":["Department of Applied Mathematics Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics Massachusetts Institute of Technology Cambridge, Massachusetts 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024148075"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":2.1804,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8757676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","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":0.9983000159263611,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9907000064849854,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9721999764442444,"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/unimodality","display_name":"Unimodality","score":0.890470027923584},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8516919612884521},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8009010553359985},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7644639611244202},{"id":"https://openalex.org/keywords/distributive-property","display_name":"Distributive property","score":0.7170364260673523},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5876612067222595},{"id":"https://openalex.org/keywords/distributive-lattice","display_name":"Distributive lattice","score":0.5353980660438538},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.5148534178733826},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3543184995651245},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1705540120601654},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07821109890937805}],"concepts":[{"id":"https://openalex.org/C21596040","wikidata":"https://www.wikidata.org/wiki/Q2896771","display_name":"Unimodality","level":2,"score":0.890470027923584},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8516919612884521},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8009010553359985},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7644639611244202},{"id":"https://openalex.org/C11821877","wikidata":"https://www.wikidata.org/wiki/Q187959","display_name":"Distributive property","level":2,"score":0.7170364260673523},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5876612067222595},{"id":"https://openalex.org/C192606457","wikidata":"https://www.wikidata.org/wiki/Q2363730","display_name":"Distributive lattice","level":3,"score":0.5353980660438538},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.5148534178733826},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3543184995651245},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1705540120601654},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07821109890937805},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1971","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1971","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n4/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":null,"license_id":null,"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:10.37236/1971","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1971","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v12i1n4/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":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":[{"display_name":"Reduced inequalities","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2999505892.pdf","grobid_xml":"https://content.openalex.org/works/W2999505892.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W640186881","https://openalex.org/W1556467361","https://openalex.org/W1734188852","https://openalex.org/W1741136470","https://openalex.org/W1893041601","https://openalex.org/W1956653947","https://openalex.org/W1976668598","https://openalex.org/W2015050395","https://openalex.org/W2029143416","https://openalex.org/W2057551462","https://openalex.org/W2058830040","https://openalex.org/W2079063393","https://openalex.org/W2111604338","https://openalex.org/W2169235006","https://openalex.org/W2914659449","https://openalex.org/W2993227358","https://openalex.org/W4237012419","https://openalex.org/W4248936574","https://openalex.org/W4248999991","https://openalex.org/W6697549010"],"related_works":["https://openalex.org/W4232534867","https://openalex.org/W2951233655","https://openalex.org/W2037861231","https://openalex.org/W2307047024","https://openalex.org/W2122961867","https://openalex.org/W2963428356","https://openalex.org/W1975062576","https://openalex.org/W871156903","https://openalex.org/W1804250731","https://openalex.org/W2126448176"],"abstract_inverted_index":{"It":[0],"is":[1],"shown":[2],"that":[3],"the":[4,13,27,45,49],"numbers":[5],"$c_i$":[6],"of":[7,9,17,22,44],"chains":[8],"length":[10,23],"$i$":[11],"in":[12],"proper":[14],"part":[15],"$L\\setminus\\{0,1\\}$":[16],"a":[18],"distributive":[19],"lattice":[20],"$L$":[21],"$\\ell":[24],"+2$":[25],"satisfy":[26],"inequalities":[28,46],"$$c_0":[29],"&lt;":[30,32],"\\ldots":[31],"c_{\\lfloor{\\ell":[33],"/2}\\rfloor}":[34],"\\quad\\hbox{":[35],"and":[36],"}\\quad":[37],"c_{\\lfloor{3":[38],"\\ell":[39],"/4}\\rfloor}&gt;\\ldots&gt;c_{\\ell}.$$":[40],"This":[41],"proves":[42],"75%":[43],"implied":[47],"by":[48],"Neggers":[50],"unimodality":[51],"conjecture.":[52]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
