{"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":{"id":"doi:10.5070/c63160419","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63160419","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf","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_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,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf","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"],"raw_orcid":null,"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"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, Oregon, U.S.A","institution_ids":["https://openalex.org/I181233156"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5022997192"],"corresponding_institution_ids":["https://openalex.org/I107639228"],"apc_list":null,"apc_paid":null,"fwci":0.4793,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50885368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"3","issue":"1","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":0.9997000098228455,"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":0.9997000098228455,"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":0.9994999766349792,"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":0.9980999827384949,"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/combinatorics","display_name":"Combinatorics","score":0.7994672656059265},{"id":"https://openalex.org/keywords/grassmannian","display_name":"Grassmannian","score":0.7381752133369446},{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.6841500997543335},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6265788078308105},{"id":"https://openalex.org/keywords/sign","display_name":"Sign (mathematics)","score":0.5735671520233154},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.44690415263175964},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4107142686843872},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35818666219711304},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.07651150226593018}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7994672656059265},{"id":"https://openalex.org/C162929932","wikidata":"https://www.wikidata.org/wiki/Q129638","display_name":"Grassmannian","level":2,"score":0.7381752133369446},{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.6841500997543335},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6265788078308105},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5735671520233154},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.44690415263175964},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4107142686843872},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35818666219711304},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07651150226593018},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.5070/c63160419","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63160419","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf","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_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,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.02786","is_oa":true,"landing_page_url":"http://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":"2331-8422","issn":["2331-8422"],"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"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt245432bz","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/245432bz","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf?t=rricqx","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorial Theory, vol 3, iss 1","raw_type":"article"}],"best_oa_location":{"id":"doi:10.5070/c63160419","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c63160419","pdf_url":"https://escholarship.org/content/qt245432bz/qt245432bz.pdf","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_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,"raw_source_name":"Combinatorial Theory","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"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3145721341.pdf"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1020681818","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/W4233168788","https://openalex.org/W4237012419","https://openalex.org/W4287867707","https://openalex.org/W4288400169","https://openalex.org/W4300302225","https://openalex.org/W4309432593","https://openalex.org/W4312186735","https://openalex.org/W4394664965"],"related_works":["https://openalex.org/W2106070061","https://openalex.org/W4297683751","https://openalex.org/W2949222060","https://openalex.org/W4298056360","https://openalex.org/W2899451587","https://openalex.org/W2067929456","https://openalex.org/W2345391861","https://openalex.org/W3190066128","https://openalex.org/W2988392988","https://openalex.org/W4309806125"],"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],"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],"Sperner.Mathematics":[173],"Subject":[174],"Classifications:":[175],"06A07,":[176],"14M15,":[177],"81T60,":[178],"05A19Keywords:":[179],"Amplituhedron,":[180],"shellability,":[181],"Eulerian":[182],"number,":[183],"log":[184],"concavity,":[185],"Sperner":[186],"property":[187]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}
