{"id":"https://openalex.org/W2965957794","doi":"https://doi.org/10.37236/8949","title":"Improved Bounds for Induced Poset Saturation","display_name":"Improved Bounds for Induced Poset Saturation","publication_year":2020,"publication_date":"2020-05-22","ids":{"openalex":"https://openalex.org/W2965957794","doi":"https://doi.org/10.37236/8949","mag":"2965957794"},"language":"en","primary_location":{"id":"doi:10.37236/8949","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8949","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p31/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p31/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081850677","display_name":"Ryan R. Martin","orcid":"https://orcid.org/0000-0003-0683-1414"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ryan R. Martin","raw_affiliation_strings":["Iowa State University","Iowa State University\u2028"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Iowa State University","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Iowa State University\u2028","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111477313","display_name":"Heather C. Smith","orcid":null},"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":false,"raw_author_name":"Heather C. Smith","raw_affiliation_strings":["Davidson College"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Davidson College","institution_ids":["https://openalex.org/I141720752"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051441025","display_name":"Shanise Walker","orcid":"https://orcid.org/0000-0001-5884-1767"},"institutions":[{"id":"https://openalex.org/I124727415","display_name":"University of Wisconsin\u2013Eau Claire","ror":"https://ror.org/03mnm0t94","country_code":"US","type":"education","lineage":["https://openalex.org/I124727415"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shanise Walker","raw_affiliation_strings":["University of Wisconsin-Eau Claire","University of Wisconsin Eau-Claire"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Eau Claire","institution_ids":["https://openalex.org/I124727415"]},{"raw_affiliation_string":"University of Wisconsin Eau-Claire","institution_ids":["https://openalex.org/I124727415"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1457,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.48897328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"27","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11567","display_name":"semigroups and automata theory","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T11130","display_name":"Coding theory and cryptography","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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":0.9779000282287598,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/partially-ordered-set","display_name":"Partially ordered set","score":0.839724063873291},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8189527988433838},{"id":"https://openalex.org/keywords/antichain","display_name":"Antichain","score":0.794306755065918},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5859810709953308},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5858176946640015},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5610271692276001},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4004725217819214},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22760850191116333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0509820282459259}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.839724063873291},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8189527988433838},{"id":"https://openalex.org/C136134351","wikidata":"https://www.wikidata.org/wiki/Q431937","display_name":"Antichain","level":3,"score":0.794306755065918},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5859810709953308},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5858176946640015},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5610271692276001},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4004725217819214},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22760850191116333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0509820282459259},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8949","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8949","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p31/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:arXiv.org:1908.01108","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1908.01108","pdf_url":"https://arxiv.org/pdf/1908.01108","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":"","raw_type":"text"},{"id":"mag:2965957794","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1908.01108.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1908.01108","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1908.01108","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/8949","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8949","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i2p31/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/G4514891127","display_name":null,"funder_award_id":"353292","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5240543169","display_name":null,"funder_award_id":"1344199","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320311090","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2965957794.pdf","grobid_xml":"https://content.openalex.org/works/W2965957794.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W2044935944","https://openalex.org/W2087567316","https://openalex.org/W2502085572","https://openalex.org/W2576813251","https://openalex.org/W6638336253","https://openalex.org/W6645723388","https://openalex.org/W6683846334"],"related_works":["https://openalex.org/W3030386554","https://openalex.org/W3202070446","https://openalex.org/W3099512742","https://openalex.org/W2520555090","https://openalex.org/W2978247833","https://openalex.org/W2962861651","https://openalex.org/W2951338341","https://openalex.org/W2788469487","https://openalex.org/W2745777152","https://openalex.org/W2172170617","https://openalex.org/W3205311113","https://openalex.org/W3009260386","https://openalex.org/W3043627167","https://openalex.org/W1682909341","https://openalex.org/W830403835","https://openalex.org/W2963497122","https://openalex.org/W3189210424","https://openalex.org/W3093537952","https://openalex.org/W1965754865","https://openalex.org/W2073104193"],"abstract_inverted_index":{"Given":[0],"a":[1,5,34,84,105],"finite":[2],"poset":[3,74],"$\\mathcal{P}$,":[4],"family":[6,48],"$\\mathcal{F}$":[7,17,32],"of":[8,21,31,36,45,108],"elements":[9],"in":[10,49],"the":[11,50,72,77,89],"Boolean":[12,52],"lattice":[13],"is":[14],"induced-$\\mathcal{P}$-saturated":[15,47],"if":[16],"contains":[18,33],"no":[19],"copy":[20,35],"$\\mathcal{P}$":[22,37],"as":[23,38,76],"an":[24,39,46],"induced":[25,40],"subposet":[26],"but":[27],"every":[28],"proper":[29],"superset":[30],"subposet.":[41],"The":[42],"minimum":[43],"size":[44],"$n$-dimensional":[51],"lattice,":[53],"denoted":[54],"$\\mathrm{sat}^*(n,\\mathcal{P})$,":[55],"was":[56],"first":[57],"studied":[58],"by":[59],"Ferrara":[60],"et":[61],"al.":[62],"(2017).":[63],"Our":[64],"work":[65],"focuses":[66],"on":[67],"strengthening":[68],"lower":[69,86,106],"bounds.":[70],"For":[71,88],"4-point":[73],"known":[75],"diamond,":[78],"we":[79,94],"prove":[80,95],"$\\mathrm{sat}^*(n,\\Diamond)\\geq\\sqrt{n}$,":[81],"improving":[82,103],"upon":[83,104],"logarithmic":[85],"bound.":[87],"antichain":[90],"with":[91],"$k+1$":[92],"elements,":[93],"$$\\mathrm{sat}^*(n,\\mathcal{A}_{k+1})\\geq":[96],"\\left(1-\\frac{1}{\\log_2k}\\right)\\frac{kn}{\\log_2":[97],"k}$$":[98],"for":[99,110],"$n$":[100],"sufficiently":[101],"large,":[102],"bound":[107],"$3n-1$":[109],"$k\\geq":[111],"3$.":[112]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
