{"id":"https://openalex.org/W2763249217","doi":"https://doi.org/10.37236/7386","title":"Universal Layered Permutations","display_name":"Universal Layered Permutations","publication_year":2018,"publication_date":"2018-08-10","ids":{"openalex":"https://openalex.org/W2763249217","doi":"https://doi.org/10.37236/7386","mag":"2763249217"},"language":"en","primary_location":{"id":"doi:10.37236/7386","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7386","pdf_url":null,"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://doi.org/10.37236/7386","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001631971","display_name":"Michael Albert","orcid":"https://orcid.org/0009-0006-0659-7743"},"institutions":[{"id":"https://openalex.org/I80281795","display_name":"University of Otago","ror":"https://ror.org/01jmxt844","country_code":"NZ","type":"education","lineage":["https://openalex.org/I80281795"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Michael Albert","raw_affiliation_strings":["University of Otago","Univ of Otago"],"affiliations":[{"raw_affiliation_string":"University of Otago","institution_ids":["https://openalex.org/I80281795"]},{"raw_affiliation_string":"Univ of Otago","institution_ids":["https://openalex.org/I80281795"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015701030","display_name":"Michael Engen","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Engen","raw_affiliation_strings":["University of Florida"],"affiliations":[{"raw_affiliation_string":"University of Florida","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018548177","display_name":"Jay Pantone","orcid":"https://orcid.org/0000-0001-7510-8540"},"institutions":[{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]},{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Jay Pantone","raw_affiliation_strings":["Dartmouth College","(Dartmouth College)"],"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]},{"raw_affiliation_string":"(Dartmouth College)","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026309695","display_name":"Vincent Vatter","orcid":"https://orcid.org/0000-0001-5713-4059"},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vincent Vatter","raw_affiliation_strings":["University of Florida"],"affiliations":[{"raw_affiliation_string":"University of Florida","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001631971"],"corresponding_institution_ids":["https://openalex.org/I80281795"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08919004,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9908999800682068,"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/computer-science","display_name":"Computer science","score":0.43273913860321045},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3505786061286926},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3500635027885437}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43273913860321045},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3505786061286926},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3500635027885437}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/7386","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7386","pdf_url":null,"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:1710.04240","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04240","pdf_url":"https://arxiv.org/pdf/1710.04240","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:2763249217","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.04240.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":"pmh:oai:epublications.marquette.edu:math_fac-1008","is_oa":true,"landing_page_url":"https://epublications.marquette.edu/math_fac/9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401682","display_name":"e-Publications@Marquette (Marquette University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102461120","host_organization_name":"Marquette University","host_organization_lineage":["https://openalex.org/I102461120"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical and Statistical Science Faculty Research and Publications","raw_type":"text"},{"id":"doi:10.48550/arxiv.1710.04240","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.04240","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:10.37236/7386","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7386","pdf_url":null,"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":[{"display_name":"Reduced inequalities","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W2010338007","https://openalex.org/W2091514779","https://openalex.org/W2137101235","https://openalex.org/W2752853835"],"related_works":["https://openalex.org/W2963829203","https://openalex.org/W2950043401","https://openalex.org/W2010338007","https://openalex.org/W2236114744","https://openalex.org/W2023684076","https://openalex.org/W1500115130","https://openalex.org/W1592706715","https://openalex.org/W1534625320","https://openalex.org/W2014721547","https://openalex.org/W2465840400","https://openalex.org/W2913306542","https://openalex.org/W2950508796","https://openalex.org/W3014316682","https://openalex.org/W3205454984","https://openalex.org/W2616848511","https://openalex.org/W2121070347","https://openalex.org/W2188349602","https://openalex.org/W2154889723","https://openalex.org/W3037624437","https://openalex.org/W2951044388"],"abstract_inverted_index":{"We":[0],"establish":[1],"an":[2],"exact":[3],"formula":[4],"for":[5],"the":[6,9],"length":[7,17],"of":[8,16,22],"shortest":[10],"permutation":[11],"containing":[12],"all":[13],"layered":[14],"permutations":[15],"$n$,":[18],"proving":[19],"a":[20],"conjecture":[21],"Gray.":[23]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}