{"id":"https://openalex.org/W4416182706","doi":"https://doi.org/10.37236/13543","title":"On the Erd\u0151s-Szekeres Problem for Convex Permutations and Orthogonally Convex Point Sets","display_name":"On the Erd\u0151s-Szekeres Problem for Convex Permutations and Orthogonally Convex Point Sets","publication_year":2025,"publication_date":"2025-11-13","ids":{"openalex":"https://openalex.org/W4416182706","doi":"https://doi.org/10.37236/13543"},"language":null,"primary_location":{"id":"doi:10.37236/13543","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13543","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p49/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p49/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025176676","display_name":"Heather Smith Blake","orcid":"https://orcid.org/0000-0001-9316-4650"},"institutions":[{"id":"https://openalex.org/I141720752","display_name":"Davidson College","ror":"https://ror.org/02f7k4z58","country_code":"US","type":"education","lineage":["https://openalex.org/I141720752"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Heather S. Blake","raw_affiliation_strings":["Davidson College"],"affiliations":[{"raw_affiliation_string":"Davidson College","institution_ids":["https://openalex.org/I141720752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005468020","display_name":"Stefan Felsner","orcid":"https://orcid.org/0000-0002-6150-1998"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Felsner","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074978124","display_name":"Rimma H\u00e4m\u00e4l\u00e4inen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rimma H\u00e4m\u00e4l\u00e4inen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046290900","display_name":"Marcin Witkowski","orcid":"https://orcid.org/0000-0003-0955-4571"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marcin Witkowski","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5025176676"],"corresponding_institution_ids":["https://openalex.org/I141720752"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.56032986,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"32","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.6665999889373779,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.6665999889373779,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.17419999837875366,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.03400000184774399,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/convex-set","display_name":"Convex set","score":0.5825999975204468},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.576200008392334},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5759999752044678},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4887999892234802},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.461899995803833},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.45159998536109924},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.44999998807907104},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.445499986410141}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8330000042915344},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8252000212669373},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5825999975204468},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.576200008392334},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5759999752044678},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4887999892234802},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.461899995803833},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.45159998536109924},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.44999998807907104},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.445499986410141},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4449999928474426},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39469999074935913},{"id":"https://openalex.org/C134912446","wikidata":"https://www.wikidata.org/wiki/Q5166516","display_name":"Convex body","level":4,"score":0.39410001039505005},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.38830000162124634},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3792000114917755},{"id":"https://openalex.org/C6018138","wikidata":"https://www.wikidata.org/wiki/Q332715","display_name":"Absolutely convex set","level":5,"score":0.36880001425743103},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.35359999537467957},{"id":"https://openalex.org/C64051489","wikidata":"https://www.wikidata.org/wiki/Q7104528","display_name":"Orthogonal convex hull","level":5,"score":0.31139999628067017},{"id":"https://openalex.org/C153046414","wikidata":"https://www.wikidata.org/wiki/Q12482","display_name":"Set theory","level":3,"score":0.3043000102043152},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2727000117301941}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/13543","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13543","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p49/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"}],"best_oa_location":{"id":"doi:10.37236/13543","is_oa":true,"landing_page_url":"https://doi.org/10.37236/13543","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v32i4p49/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":[],"funders":[{"id":"https://openalex.org/F4320314997","display_name":"Strong","ror":"https://ror.org/041vyzr56"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416182706.pdf","grobid_xml":"https://content.openalex.org/works/W4416182706.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0,113],"finite":[1,124],"set":[2,20,41,126],"of":[3,42,50,84,98,127,134,145,151],"points":[4,10,44,128],"is":[5,21,62,115,119,136],"generic":[6,40,125],"if":[7,24,117],"no":[8],"two":[9],"are":[11],"on":[12],"the":[13,33,66,82,95,102,138],"same":[14],"vertical":[15],"or":[16],"horizontal":[17],"line.":[18],"The":[19,132],"orthogonally":[22,47],"convex":[23,48,116,130,149],"every":[25,39,143],"point":[26,99],"has":[27],"an":[28],"empty":[29],"quadrant.":[30],"We":[31],"study":[32],"smallest":[34,139],"integer":[35],"$N_o(n)$":[36,43,135],"such":[37,141],"that":[38,142],"contains":[45,147],"a":[46,110,123,148],"subset":[49],"size":[51,152],"$n$.":[52,153],"For":[53],"even":[54],"$n$,":[55],"we":[56,69,80],"prove":[57,77],"$N_0(n)":[58],"=":[59],"\\frac{1}{8}(n^2+2n+8)$,":[60],"which":[61],"tight,":[63],"and":[64,73,86,89],"in":[65,101,109,129],"odd":[67],"case":[68],"get":[70],"close":[71],"upper":[72],"lower":[74],"bounds.":[75],"To":[76],"these":[78],"results,":[79],"apply":[81],"theory":[83],"Greene":[85],"Kleitman":[87],"(1976)":[88],"Frank":[90],"(1980)":[91],"about":[92],"posets":[93],"to":[94,107,122],"partial":[96],"order":[97,120],"sets":[100,105],"plane.":[103],"Generic":[104],"correspond":[106],"permutations":[108],"canonical":[111],"way.":[112],"permutation":[114,144],"it":[118],"isomorphic":[121],"position.":[131],"value":[133],"also":[137],"$N$":[140,146],"subpermutation":[150]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-11-13T00:00:00"}
