{"id":"https://openalex.org/W3047746738","doi":"https://doi.org/10.37236/9801","title":"Sign Variation and Descents","display_name":"Sign Variation and Descents","publication_year":2020,"publication_date":"2020-12-24","ids":{"openalex":"https://openalex.org/W3047746738","doi":"https://doi.org/10.37236/9801","mag":"3047746738"},"language":"en","primary_location":{"id":"doi:10.37236/9801","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9801","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p50/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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p50/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Nantel Bergeron","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nantel Bergeron","raw_affiliation_strings":["Department of Mathematics and Statistics York University Toronto, ON, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics York University Toronto, ON, U.S.A","institution_ids":[]}]},{"author_position":"middle","author":{"id":null,"display_name":"Aram Dermenjian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aram Dermenjian","raw_affiliation_strings":["Department of Mathematics and Statistics York University Toronto, ON, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics York University Toronto, ON, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"John Machacek","orcid":null},"institutions":[{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Machacek","raw_affiliation_strings":["Michigan State University"],"affiliations":[{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":0.24638128,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"4","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":0.8967999815940857,"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":0.8967999815940857,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.03819999843835831,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.025800000876188278,"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/eulerian-path","display_name":"Eulerian path","score":0.6766999959945679},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.66839998960495},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5995000004768372},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.5286999940872192},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5127000212669373},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.47839999198913574},{"id":"https://openalex.org/keywords/variation","display_name":"Variation (astronomy)","score":0.4684999883174896}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8805999755859375},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.6766999959945679},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.66839998960495},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6406999826431274},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5995000004768372},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5286999940872192},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5127000212669373},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.47839999198913574},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.4684999883174896},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45509999990463257},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C27851653","wikidata":"https://www.wikidata.org/wiki/Q829653","display_name":"Bounded variation","level":2,"score":0.3790999948978424},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C138890893","wikidata":"https://www.wikidata.org/wiki/Q620006","display_name":"Order type","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C2777044963","wikidata":"https://www.wikidata.org/wiki/Q5384707","display_name":"Equivalence class (music)","level":2,"score":0.26019999384880066}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/9801","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9801","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p50/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:pure.atira.dk:openaire_cris_publications/0cd16761-78ae-47ec-89dd-8394dfbb5a53","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/0cd16761-78ae-47ec-89dd-8394dfbb5a53","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Bergeron, N, Dermenjian, A & Machacek, J 2020, 'Sign Variation and Descents', The Electronic Journal of Combinatorics, vol. 27, no. 4, P4.50 . https://doi.org/10.37236/9801","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2008.03794","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2008.03794","pdf_url":"https://arxiv.org/pdf/2008.03794","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"}],"best_oa_location":{"id":"doi:10.37236/9801","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9801","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p50/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":[{"id":"https://openalex.org/G5784215521","display_name":null,"funder_award_id":"Chair","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320319918","display_name":"York University","ror":"https://ror.org/05fq50484"},{"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/W3047746738.pdf","grobid_xml":"https://content.openalex.org/works/W3047746738.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1503594324","https://openalex.org/W2128843758","https://openalex.org/W2162305901"],"related_works":[],"abstract_inverted_index":{"For":[0],"any":[1],"$n":[2],">":[3],"0$":[4],"and":[5,90,129],"$0":[6],"\\leq":[7],"m":[8],"<":[9],"n$,":[10],"let":[11],"$P_{n,m}$":[12],"be":[13,42,118],"the":[14,36,43,52,74,96,110,113,119],"poset":[15],"of":[16,20,22,35,38,46,76,79,95,112,123,154,161],"projective":[17],"equivalence":[18],"classes":[19],"$\\{-,0,+\\}$-vectors":[21],"length":[23],"$n$":[24],"with":[25,144],"sign":[26],"variation":[27],"bounded":[28],"by":[29,32,127],"$m$,":[30],"ordered":[31],"reverse":[33],"inclusion":[34],"positions":[37],"zeros.":[39],"Let":[40],"$\\Delta_{n,m}$":[41,57,77,87],"order":[44],"complex":[45],"$P_{n,m}$.":[47],"A":[48],"previous":[49],"result":[50,84,143],"from":[51],"third":[53],"author":[54],"shows":[55],"that":[56,73,86],"is":[58,64,88,100],"Cohen-Macaulay":[59],"over":[60],"$\\mathbb{Q}$":[61],"whenever":[62],"$m$":[63,99],"even":[65,101],"or":[66,102],"$m":[67,103,107],"=":[68,104,108],"n-1$.":[69,105],"Hence,":[70],"it":[71],"follows":[72],"$h$-vector":[75,97,114],"consists":[78],"nonnegative":[80],"entries.":[81],"Our":[82],"main":[83,142],"states":[85],"partitionable":[89],"we":[91],"give":[92,150],"an":[93],"interpretation":[94],"when":[98],"When":[106],"n-1$":[109],"entries":[111],"turn":[115],"out":[116],"to":[117,149],"new":[120],"Eulerian":[121,159],"numbers":[122,160],"type":[124,162],"$D$":[125],"studied":[126],"Borowiec":[128],"M\u0142otkowski":[130],"in":[131],"[":[132],"Electron.":[133],"J.":[134],"Combin.,":[135],"23(1):#P1.38,":[136],"2016].":[137],"We":[138],"then":[139],"combine":[140],"our":[141],"Klee's":[145],"generalized":[146],"Dehn-Sommerville":[147],"relations":[148],"a":[151],"geometric":[152],"proof":[153],"some":[155],"facts":[156],"about":[157],"these":[158],"$D$.":[163]},"counts_by_year":[],"updated_date":"2026-04-15T08:11:43.952461","created_date":"2020-08-13T00:00:00"}