{"id":"https://openalex.org/W1863689192","doi":"https://doi.org/10.37236/2126","title":"Poset Pinball, Highest Forms, and $(n-2,2)$ Springer Varieties","display_name":"Poset Pinball, Highest Forms, and $(n-2,2)$ Springer Varieties","publication_year":2012,"publication_date":"2012-03-19","ids":{"openalex":"https://openalex.org/W1863689192","doi":"https://doi.org/10.37236/2126","mag":"1863689192"},"language":"en","primary_location":{"id":"doi:10.37236/2126","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2126","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p56/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/v19i1p56/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025916926","display_name":"Barry Dewitt","orcid":"https://orcid.org/0000-0003-1622-6736"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Barry Dewitt","raw_affiliation_strings":["McMaster University Hamilton, Canada","Department of Mathematics and Statistics","Mathematical Institute University of Oxford Oxford, U.K"],"affiliations":[{"raw_affiliation_string":"McMaster University Hamilton, Canada","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"Mathematical Institute University of Oxford Oxford, U.K","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001770867","display_name":"Megumi Harada","orcid":"https://orcid.org/0000-0001-8939-7531"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Megumi Harada","raw_affiliation_strings":["Mathematical Institute University of Oxford Oxford, U.K","McMaster University Hamilton, Canada","Department of Mathematics and Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematical Institute University of Oxford Oxford, U.K","institution_ids":[]},{"raw_affiliation_string":"McMaster University Hamilton, Canada","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025916926"],"corresponding_institution_ids":["https://openalex.org/I98251732"],"apc_list":null,"apc_paid":null,"fwci":2.9328,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.89168245,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9990000128746033,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9940999746322632,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8599644899368286},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.730296790599823},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6161180734634399},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.5695667266845703},{"id":"https://openalex.org/keywords/equivariant-map","display_name":"Equivariant map","score":0.5470002293586731},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.5181542634963989},{"id":"https://openalex.org/keywords/nilpotent","display_name":"Nilpotent","score":0.47278547286987305},{"id":"https://openalex.org/keywords/equivariant-cohomology","display_name":"Equivariant cohomology","score":0.4627746343612671},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4609238803386688},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.45110926032066345},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4280863106250763},{"id":"https://openalex.org/keywords/cohomology","display_name":"Cohomology","score":0.4272055923938751},{"id":"https://openalex.org/keywords/nilpotent-matrix","display_name":"Nilpotent matrix","score":0.41614076495170593},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.41560420393943787},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.41156303882598877},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21888142824172974},{"id":"https://openalex.org/keywords/square-matrix","display_name":"Square matrix","score":0.21332725882530212},{"id":"https://openalex.org/keywords/symmetric-matrix","display_name":"Symmetric matrix","score":0.0972331166267395}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8599644899368286},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.730296790599823},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6161180734634399},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5695667266845703},{"id":"https://openalex.org/C171036898","wikidata":"https://www.wikidata.org/wiki/Q256355","display_name":"Equivariant map","level":2,"score":0.5470002293586731},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.5181542634963989},{"id":"https://openalex.org/C50555996","wikidata":"https://www.wikidata.org/wiki/Q840023","display_name":"Nilpotent","level":2,"score":0.47278547286987305},{"id":"https://openalex.org/C72738302","wikidata":"https://www.wikidata.org/wiki/Q5384738","display_name":"Equivariant cohomology","level":3,"score":0.4627746343612671},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4609238803386688},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.45110926032066345},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4280863106250763},{"id":"https://openalex.org/C78606066","wikidata":"https://www.wikidata.org/wiki/Q1198376","display_name":"Cohomology","level":2,"score":0.4272055923938751},{"id":"https://openalex.org/C27563320","wikidata":"https://www.wikidata.org/wiki/Q650670","display_name":"Nilpotent matrix","level":5,"score":0.41614076495170593},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.41560420393943787},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.41156303882598877},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21888142824172974},{"id":"https://openalex.org/C69044650","wikidata":"https://www.wikidata.org/wiki/Q2739329","display_name":"Square matrix","level":4,"score":0.21332725882530212},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.0972331166267395},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/2126","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2126","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p56/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.226.7518","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.226.7518","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/ojs/index.php/eljc/article/download/v19i1p56/pdf/","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/2126","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2126","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i1p56/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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320336370","display_name":"Ontario Ministry of Research and Innovation","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1863689192.pdf","grobid_xml":"https://content.openalex.org/works/W1863689192.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1652980716","https://openalex.org/W1925057626","https://openalex.org/W1934831339","https://openalex.org/W1993550436","https://openalex.org/W2012323075","https://openalex.org/W2015351041","https://openalex.org/W2022298965","https://openalex.org/W2056721026","https://openalex.org/W2064160339","https://openalex.org/W2082571435","https://openalex.org/W2085888974","https://openalex.org/W2128387932","https://openalex.org/W2171365210","https://openalex.org/W2325453580","https://openalex.org/W2953021841","https://openalex.org/W2964076392"],"related_works":["https://openalex.org/W2046926085","https://openalex.org/W2000585582","https://openalex.org/W4249807130","https://openalex.org/W3111598482","https://openalex.org/W2070214232","https://openalex.org/W4249922773","https://openalex.org/W1970411947","https://openalex.org/W198388172","https://openalex.org/W1863689192","https://openalex.org/W2951403823"],"abstract_inverted_index":{"In":[0],"this":[1,220],"manuscript":[2],"we":[3,46,70,100,127,161],"study":[4,140],"type":[5,145],"$A$":[6,146],"nilpotent":[7,32,93,111],"Hessenberg":[8,97,112],"varieties":[9,34,148],"equipped":[10],"with":[11,23,59,62,262],"a":[12,24,28,56,92,177,199,240,254],"natural":[13],"$S^1$-action":[14],"using":[15],"techniques":[16],"introduced":[17,134],"by":[18,135,171],"Tymoczko,":[19,138],"Harada-Tymoczko,":[20],"and":[21,74,96,115,137,173,242],"Bayegan-Harada,":[22],"particular":[25],"emphasis":[26],"on":[27],"special":[29],"class":[30],"of":[31,55,82,88,109,118,121,144,154,179,188,202,233,245],"Springer":[33,147],"corresponding":[35,51],"to":[36,52,139,151,175,198,253],"the":[37,48,63,67,106,110,116,122,131,141,163,180,185,189,205,222,228],"partition":[38],"$\\lambda=":[39],"(n-2,2)$":[40],"for":[41,91,157,167,258,265],"$n":[42],"\\geq":[43],"4$.":[44,159],"First":[45],"define":[47],"adjacent-pair":[49,68],"matrix":[50,69],"any":[53],"filling":[54],"Young":[57,123,152],"diagram":[58,124],"$n$":[60],"boxes":[61],"alphabet":[64],"$\\{1,2,\\ldots,n\\}$.":[65],"Using":[66],"make":[71],"more":[72],"explicit":[73,103,243],"also":[75],"extend":[76],"some":[77],"statements":[78],"concerning":[79],"highest":[80],"forms":[81],"linear":[83],"operators":[84],"in":[85,184,227],"previous":[86],"work":[87],"Tymoczko.":[89],"Second,":[90],"operator":[94],"$N$":[95],"function":[98],"$h$,":[99],"construct":[101],"an":[102],"bijection":[104],"between":[105],"$S^1$-fixed":[107],"points":[108],"variety":[113,191],"Hess$(N,h)$":[114],"set":[117],"$(h,\\lambda_N)$-permissible":[119],"fillings":[120],"$\\lambda_N$.":[125],"Third,":[126],"use":[128,162],"poset":[129,213,250],"pinball,":[130],"combinatorial":[132],"game":[133],"Harada":[136,174],"$S^1$-equivariant":[142],"cohomology":[143,187],"$\\mathcal{S}_{(n-2,2)}$":[149],"associated":[150],"diagrams":[153],"shape":[155],"$(n-2,2)$":[156],"$n\\geq":[158],"Specifically,":[160],"dimension":[164],"pair":[165],"algorithm":[166],"Betti-acceptable":[168],"pinball":[169,214,251],"described":[170],"Bayegan":[172],"specify":[176],"subset":[178],"equivariant":[181],"Schubert":[182],"classes":[183],"$\\mathbb{T}$-equivariant":[186],"flag":[190],"$\\mathcal{F}\\ell":[192],"ags(\\mathbb{C}^n)":[193],"\\cong":[194],"GL(n,\\mathbb{C})/B$":[195],"which":[196,247],"maps":[197],"module":[200,215,256],"basis":[201,216,246,252,257],"$H^*_{S^1}(\\mathcal{S}_{(n-2,2)})$":[203],"under":[204],"projection":[206],"map":[207],"$H^*_\\mathbb{T}(\\mathcal{F}\\ell":[208],"ags(\\mathbb{C}^n))":[209],"\\to":[210],"H^*_{S^1}(\\mathcal{S}_{(n-2,2)})$.":[211],"Our":[212],"is":[217,221,236],"not":[218],"poset-upper-triangular;":[219],"first":[223],"concrete":[224],"such":[225],"example":[226],"literature.":[229],"A":[230],"straightforward":[231],"consequence":[232],"our":[234,249],"proof":[235],"that":[237],"there":[238],"exists":[239],"simple":[241],"change":[244],"transforms":[248],"poset-upper-triangular":[255],"$H^*_{S^1}(\\mathcal{S}_{(n-2,2)})$.":[259],"We":[260],"close":[261],"open":[263],"questions":[264],"future":[266],"work.":[267]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
