{"id":"https://openalex.org/W3145721341","doi":"https://doi.org/10.5070/c63160419","title":"Shelling the \\(m=1\\) amplituhedron","display_name":"Shelling the \\(m=1\\) amplituhedron","publication_year":2023,"publication_date":"2023-03-14","ids":{"openalex":"https://openalex.org/W3145721341","doi":"https://doi.org/10.5070/c63160419","mag":"3145721341"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.5070/c63160419","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf?t=rricqx","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf?t=rricqx","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022997192","display_name":"Steven N. Karp","orcid":"https://orcid.org/0000-0001-7163-667X"},"institutions":[{"id":"https://openalex.org/I107639228","display_name":"University of Notre Dame","ror":"https://ror.org/00mkhxb43","country_code":"US","type":"education","lineage":["https://openalex.org/I107639228"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Steven N. Karp","raw_affiliation_strings":["Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, U.S.A."],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Notre Dame, Notre Dame, Indiana, U.S.A.","institution_ids":["https://openalex.org/I107639228"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029369206","display_name":"John Machacek","orcid":"https://orcid.org/0000-0001-9087-4964"},"institutions":[{"id":"https://openalex.org/I181233156","display_name":"University of Oregon","ror":"https://ror.org/0293rh119","country_code":"US","type":"education","lineage":["https://openalex.org/I181233156"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Machacek","raw_affiliation_strings":["Department of Mathematics, University of Oregon, Eugene, Oregon, U.S.A."],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, Oregon, U.S.A.","institution_ids":["https://openalex.org/I181233156"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022997192"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":{"value":0,"currency":"USD","value_usd":0,"provenance":"doaj"},"apc_paid":null,"fwci":0.781,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":2,"citation_normalized_percentile":{"value":0.549866,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":78,"max":84},"biblio":{"volume":"3","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9997,"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":0.9997,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9995,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9981,"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":[],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.79946727},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.7381752},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6841501},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6265788},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.57356715},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.44690415},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41071427},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35818666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0765115},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.5070/c63160419","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf?t=rricqx","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},{"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2104.02786","pdf_url":"https://arxiv.org/pdf/2104.02786","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_indexed_in_scopus":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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.5070/c63160419","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf?t=rricqx","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_indexed_in_scopus":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":34,"referenced_works":["https://openalex.org/W1515761639","https://openalex.org/W1537957332","https://openalex.org/W1672638072","https://openalex.org/W1818457196","https://openalex.org/W1972297736","https://openalex.org/W1974343630","https://openalex.org/W2001367217","https://openalex.org/W2015050395","https://openalex.org/W2072578197","https://openalex.org/W2087567316","https://openalex.org/W2118624390","https://openalex.org/W2166935116","https://openalex.org/W2224932111","https://openalex.org/W2405154940","https://openalex.org/W2963046719","https://openalex.org/W2964082626","https://openalex.org/W2964682601","https://openalex.org/W2972915661","https://openalex.org/W2972964267","https://openalex.org/W3005689826","https://openalex.org/W3037609493","https://openalex.org/W3080247059","https://openalex.org/W3087197810","https://openalex.org/W3104493577","https://openalex.org/W3117097825","https://openalex.org/W3155723035","https://openalex.org/W3159280975","https://openalex.org/W4205396504","https://openalex.org/W4237012419","https://openalex.org/W4287867707","https://openalex.org/W4300302225","https://openalex.org/W4309432593","https://openalex.org/W4312186735","https://openalex.org/W4394664965"],"related_works":["https://openalex.org/W4309806125","https://openalex.org/W4298056360","https://openalex.org/W4297683751","https://openalex.org/W3190066128","https://openalex.org/W2988392988","https://openalex.org/W2949222060","https://openalex.org/W2899451587","https://openalex.org/W2345391861","https://openalex.org/W2106070061","https://openalex.org/W2067929456"],"abstract_inverted_index":{"The":[0],"amplituhedron":[1,49],"$\\mathcal{A}_{n,k,m}$":[2],"was":[3,108],"introduced":[4,143],"by":[5,90,111,144],"Arkani-Hamed":[6],"and":[7,43,92,113,123,127,133,168],"Trnka":[8],"(2014)":[9],"in":[10,21],"order":[11],"to":[12,103],"give":[13,117],"a":[14,29,52,87,96,104,139],"geometric":[15],"basis":[16],"for":[17,120],"calculating":[18],"scattering":[19],"amplitudes":[20],"planar":[22],"$\\mathcal{N}=4$":[23],"supersymmetric":[24],"Yang-Mills":[25],"theory.":[26],"It":[27],"is":[28,84,101,131,166,172],"projection":[30],"inside":[31],"the":[32,36,47,121],"Grassmannian":[33],"$\\text{Gr}_{k,k+m}$":[34],"of":[35,40,56,67,72,125,148,153],"totally":[37],"nonnegative":[38],"part":[39],"$\\text{Gr}_{k,n}$.":[41],"Karp":[42,91,112],"Williams":[44],"(2019)":[45],"studied":[46],"$m=1$":[48],"$\\mathcal{A}_{n,k,1}$,":[50],"giving":[51],"regular":[53],"CW":[54],"decomposition":[55],"it.":[57],"Its":[58],"face":[59],"poset":[60,141],"$R_{n,l}$":[61,83],"(with":[62],"$l":[63],":=":[64],"n-k-1$)":[65],"consists":[66],"all":[68,149],"projective":[69,150],"sign":[70,78,151,160],"vectors":[71,152],"length":[73,154],"$n$":[74,155],"with":[75,156],"exactly":[76],"$l$":[77,159],"changes.":[79,161],"We":[80,115,162],"show":[81,128,163],"that":[82,99,129,164,170],"EL-shellable,":[85],"resolving":[86],"problem":[88],"posed":[89],"Williams.":[93,114],"This":[94],"gives":[95],"new":[97],"proof":[98],"$\\mathcal{A}_{n,k,1}$":[100],"homeomorphic":[102],"closed":[105],"ball,":[106],"which":[107],"originally":[109],"proved":[110],"also":[116],"explicit":[118],"formulas":[119],"$f$-vector":[122],"$h$-vector":[124],"$R_{n,l}$,":[126],"it":[130,165,171],"rank-log-concave":[132],"strongly":[134],"Sperner.":[135,173],"Finally,":[136],"we":[137],"consider":[138],"related":[140],"$P_{n,l}$":[142],"Machacek":[145],"(2019),":[146],"consisting":[147],"at":[157],"most":[158],"rank-log-concave,":[167],"conjecture":[169]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3145721341","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-01-23T03:47:21.916553","created_date":"2021-04-13"}