{"id":"https://openalex.org/W2129688665","doi":"https://doi.org/10.37236/1092","title":"Permutation Reconstruction from Minors","display_name":"Permutation Reconstruction from Minors","publication_year":2006,"publication_date":"2006-08-03","ids":{"openalex":"https://openalex.org/W2129688665","doi":"https://doi.org/10.37236/1092","mag":"2129688665"},"language":"en","primary_location":{"id":"doi:10.37236/1092","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1092","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r66/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":null,"license_id":null,"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/v13i1r66/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089603958","display_name":"Mariana Raykova","orcid":"https://orcid.org/0000-0002-1744-4025"},"institutions":[{"id":"https://openalex.org/I39661318","display_name":"Bard College","ror":"https://ror.org/04yrgt058","country_code":"US","type":"education","lineage":["https://openalex.org/I39661318"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mariana Raykova","raw_affiliation_strings":["Bard College Annandale-on-Hudson, NY 12504, USA","Bard College"],"affiliations":[{"raw_affiliation_string":"Bard College Annandale-on-Hudson, NY 12504, USA","institution_ids":["https://openalex.org/I39661318"]},{"raw_affiliation_string":"Bard College","institution_ids":["https://openalex.org/I39661318"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089603958"],"corresponding_institution_ids":["https://openalex.org/I39661318"],"apc_list":null,"apc_paid":null,"fwci":1.1658,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.80240426,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"13","issue":"1","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":0.9973000288009644,"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":0.9973000288009644,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9883999824523926,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9771000146865845,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiset","display_name":"Multiset","score":0.9624052047729492},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8844909071922302},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8212442398071289},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.7640080451965332},{"id":"https://openalex.org/keywords/parity-of-a-permutation","display_name":"Parity of a permutation","score":0.4767818748950958},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4413191080093384},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4249926507472992},{"id":"https://openalex.org/keywords/cyclic-permutation","display_name":"Cyclic permutation","score":0.39009299874305725},{"id":"https://openalex.org/keywords/symmetric-group","display_name":"Symmetric group","score":0.13984662294387817}],"concepts":[{"id":"https://openalex.org/C2779623528","wikidata":"https://www.wikidata.org/wiki/Q864377","display_name":"Multiset","level":2,"score":0.9624052047729492},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8844909071922302},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8212442398071289},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.7640080451965332},{"id":"https://openalex.org/C64137656","wikidata":"https://www.wikidata.org/wiki/Q1064405","display_name":"Parity of a permutation","level":4,"score":0.4767818748950958},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4413191080093384},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4249926507472992},{"id":"https://openalex.org/C77670614","wikidata":"https://www.wikidata.org/wiki/Q212130","display_name":"Cyclic permutation","level":3,"score":0.39009299874305725},{"id":"https://openalex.org/C128622974","wikidata":"https://www.wikidata.org/wiki/Q849512","display_name":"Symmetric group","level":2,"score":0.13984662294387817},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1092","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1092","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r66/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.175.9677","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.175.9677","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_13/PDF/v13i1r66.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.505.2873","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.505.2873","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.columbia.edu/~mariana/papers/perm_reconstruct.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1092","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1092","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v13i1r66/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":null,"license_id":null,"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/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320311182","display_name":"Bard College","ror":"https://ror.org/04yrgt058"},{"id":"https://openalex.org/F4320311500","display_name":"University of Minnesota Duluth","ror":"https://ror.org/01hy4qx27"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2129688665.pdf","grobid_xml":"https://content.openalex.org/works/W2129688665.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W93757924","https://openalex.org/W188669452","https://openalex.org/W1533006072","https://openalex.org/W4212838771","https://openalex.org/W4250666656"],"related_works":["https://openalex.org/W2964309395","https://openalex.org/W3184996090","https://openalex.org/W2140809923","https://openalex.org/W4379261363","https://openalex.org/W4251766710","https://openalex.org/W4319792903","https://openalex.org/W4285292213","https://openalex.org/W2949607517","https://openalex.org/W3208073225","https://openalex.org/W2518260394"],"abstract_inverted_index":{"We":[0,37,66,84,109,150],"consider":[1],"the":[2,39,46,50,68,111,126,130,145,156],"problem":[3],"of":[4,11,18,24,49,70,82,107,141],"permutation":[5,16,96],"reconstruction,":[6],"which":[7],"is":[8,102],"a":[9,15,58],"variant":[10],"graph":[12],"reconstruction.":[13],"Given":[14],"$p$":[17,75],"length":[19,98,132],"$n$,":[20],"we":[21,72,143,159],"delete":[22],"$k$":[23,92],"its":[25,77,80,105],"entries":[26],"in":[27,155],"each":[28],"possible":[29],"way":[30],"to":[31,43,52,135,162],"obtain":[32],"${n":[33],"\\choose":[34],"k}$":[35],"subsequences.":[36],"renumber":[38],"sequences":[40],"from":[41,76,104,138],"$1$":[42],"$n-k$":[44],"preserving":[45],"relative":[47],"size":[48],"elements":[51],"form":[53,57],"$(n-k)$-minors.":[54,108],"These":[55],"minors":[56],"multiset":[59,78,106],"$M_k(p)$":[60],"with":[61,97],"an":[62,88],"underlying":[63],"set":[64,81],"$M_k'(p)$.":[65],"study":[67],"question":[69],"when":[71,158],"can":[73],"reconstruct":[74],"or":[79],"minors.":[83],"prove":[85],"there":[86],"exists":[87],"$N_k$":[89,101],"for":[90,133],"every":[91],"such":[93],"that":[94],"any":[95],"at":[99],"least":[100],"reconstructible":[103,137],"find":[110],"bounds":[112,154],"$N_k":[113,118],">":[114,148],"k+\\log_2":[115],"k$":[116],"and":[117],"<":[119],"{k^2\\over4}":[120],"+":[121,123],"2k":[122],"4$.":[124],"For":[125],"number":[127],"$N_k'$,":[128],"giving":[129],"minimal":[131],"permutations":[134],"be":[136],"their":[139],"sets":[140],"$(n-k)$-minors,":[142],"have":[144],"bound":[146],"$N_k'":[147],"2k$.":[149],"work":[151],"towards":[152],"analogous":[153],"case":[157],"restrict":[160],"ourselves":[161],"layered":[163],"permutations.":[164]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}