{"id":"https://openalex.org/W2198492702","doi":"https://doi.org/10.37236/5353","title":"Reconstructing Permutations from Identification Minors","display_name":"Reconstructing Permutations from Identification Minors","publication_year":2015,"publication_date":"2015-10-30","ids":{"openalex":"https://openalex.org/W2198492702","doi":"https://doi.org/10.37236/5353","mag":"2198492702"},"language":"en","primary_location":{"id":"doi:10.37236/5353","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5353","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p20/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/v22i4p20/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075775895","display_name":"Erkko Lehtonen","orcid":"https://orcid.org/0000-0002-9255-5876"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"TU Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Erkko Lehtonen","raw_affiliation_strings":["Technische Universit\u00e4t Dresden"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Dresden","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5075775895"],"corresponding_institution_ids":["https://openalex.org/I78650965"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.07898917,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"22","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.8611000180244446,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.8611000180244446,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.771399974822998,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.7328000068664551,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.8324373364448547},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7546976804733276},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7399969100952148},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7214053869247437},{"id":"https://openalex.org/keywords/identification","display_name":"Identification (biology)","score":0.6412639617919922},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6325883269309998},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4579014778137207},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4202394187450409},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17809811234474182}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.8324373364448547},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7546976804733276},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7399969100952148},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7214053869247437},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.6412639617919922},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6325883269309998},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4579014778137207},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4202394187450409},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17809811234474182},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5353","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5353","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p20/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:10.37236/5353","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5353","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p20/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/G2549560045","display_name":null,"funder_award_id":"UID/Multi/04621/2013","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"},{"id":"https://openalex.org/G8253700035","display_name":null,"funder_award_id":"University of Lisbon","funder_id":"https://openalex.org/F4320334779","funder_display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia"}],"funders":[{"id":"https://openalex.org/F4320321613","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30"},{"id":"https://openalex.org/F4320323424","display_name":"Universidade de Lisboa","ror":"https://ror.org/01c27hj86"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2198492702.pdf","grobid_xml":"https://content.openalex.org/works/W2198492702.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W188669452","https://openalex.org/W1533006072","https://openalex.org/W1592211005","https://openalex.org/W1985792271","https://openalex.org/W1988557549","https://openalex.org/W2001302292","https://openalex.org/W2003824380","https://openalex.org/W2020661143","https://openalex.org/W2118644061","https://openalex.org/W2129688665","https://openalex.org/W2150109348","https://openalex.org/W2151916942","https://openalex.org/W2163511203","https://openalex.org/W2963920170","https://openalex.org/W3099428344","https://openalex.org/W4250666656","https://openalex.org/W6647276136"],"related_works":["https://openalex.org/W3162204513","https://openalex.org/W2371138613","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W2239445980","https://openalex.org/W2995553446","https://openalex.org/W2120455979","https://openalex.org/W2142539551"],"abstract_inverted_index":{"We":[0,64],"consider":[1],"the":[2,76],"problem":[3],"whether":[4],"a":[5,8,38,59,67],"permutation":[6,36,60],"of":[7,23,37,69],"finite":[9,39],"set":[10,25,40],"is":[11,46],"uniquely":[12],"determined":[13],"by":[14],"its":[15,49,62],"identification":[16,50],"minors.":[17,51],"While":[18],"there":[19],"exist":[20],"non-reconstructible":[21],"permutations":[22],"every":[24,35],"with":[26,41],"two,":[27],"three,":[28],"or":[29],"four":[30],"elements,":[31],"we":[32,53],"show":[33],"that":[34],"at":[42],"least":[43],"five":[44],"elements":[45],"reconstructible":[47],"from":[48,61],"Moreover,":[52],"provide":[54],"an":[55],"algorithm":[56],"for":[57],"recovering":[58],"deck.":[63],"also":[65],"discuss":[66],"generalization":[68],"this":[70],"reconstruction":[71],"problem,":[72],"as":[73,75],"well":[74],"related":[77],"set-reconstruction":[78],"problem.":[79]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}