{"id":"https://openalex.org/W2902236522","doi":"https://doi.org/10.1142/s1793830920500147","title":"Quantifying CDS sortability of permutations by strategic pile size","display_name":"Quantifying CDS sortability of permutations by strategic pile size","publication_year":2019,"publication_date":"2019-11-18","ids":{"openalex":"https://openalex.org/W2902236522","doi":"https://doi.org/10.1142/s1793830920500147","mag":"2902236522"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830920500147","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830920500147","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1811.11937","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005291131","display_name":"Marisa Gaetz","orcid":"https://orcid.org/0000-0001-8798-1435"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Marisa Gaetz","raw_affiliation_strings":["Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA","Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02139, USA"],"raw_orcid":"https://orcid.org/0000-0001-8798-1435","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035986204","display_name":"Bethany Flanagan","orcid":null},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bethany Flanagan","raw_affiliation_strings":["Department of Mathematics, Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA","Department of Mathematics, Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA","institution_ids":["https://openalex.org/I219193219"]},{"raw_affiliation_string":"Department of Mathematics, Purdue University, 610 Purdue Mall, West Lafayette, IN 47907, USA#TAB#","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060683305","display_name":"Marion Scheepers","orcid":"https://orcid.org/0000-0001-8037-8158"},"institutions":[{"id":"https://openalex.org/I120156002","display_name":"Boise State University","ror":"https://ror.org/02e3zdp86","country_code":"US","type":"education","lineage":["https://openalex.org/I120156002"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marion Scheepers","raw_affiliation_strings":["Department of Mathematics, Boise State University, 1910 West University Dr, Boise, ID 83725, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Boise State University, 1910 West University Dr, Boise, ID 83725, USA","institution_ids":["https://openalex.org/I120156002"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022026321","display_name":"Meghan Shanks","orcid":"https://orcid.org/0000-0003-4890-1302"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meghan Shanks","raw_affiliation_strings":["Department of Computer Science, University of Illinois at Urbana\u2013Champaign, 201 N Goodwin Ave, Urbana, IL 61801, USA","Department of Computer Science, University of Illinois at Urbana-Champaign, 201 N. Goodwin Ave., Urbana, IL, 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana\u2013Champaign, 201 N Goodwin Ave, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Department of Computer Science, University of Illinois at Urbana-Champaign, 201 N. Goodwin Ave., Urbana, IL, 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5005291131"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00333751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"12","issue":"01","first_page":"2050014","last_page":"2050014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13664","display_name":"Genome Rearrangement Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9923999905586243,"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/T10015","display_name":"Genomics and Phylogenetic Studies","score":0.9843999743461609,"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":0.6725051999092102},{"id":"https://openalex.org/keywords/sorting","display_name":"Sorting","score":0.6543722748756409},{"id":"https://openalex.org/keywords/pile","display_name":"Pile","score":0.6183484196662903},{"id":"https://openalex.org/keywords/merge","display_name":"Merge (version control)","score":0.580501139163971},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5301460027694702},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47040849924087524},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4154886305332184},{"id":"https://openalex.org/keywords/coalescent-theory","display_name":"Coalescent theory","score":0.41481342911720276},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34120726585388184},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32827746868133545},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22282153367996216},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19235825538635254},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.1646328866481781},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.13888803124427795},{"id":"https://openalex.org/keywords/gene","display_name":"Gene","score":0.06740853190422058},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.06651830673217773}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6725051999092102},{"id":"https://openalex.org/C111696304","wikidata":"https://www.wikidata.org/wiki/Q2303697","display_name":"Sorting","level":2,"score":0.6543722748756409},{"id":"https://openalex.org/C119560385","wikidata":"https://www.wikidata.org/wiki/Q7193850","display_name":"Pile","level":2,"score":0.6183484196662903},{"id":"https://openalex.org/C197129107","wikidata":"https://www.wikidata.org/wiki/Q1921621","display_name":"Merge (version control)","level":2,"score":0.580501139163971},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5301460027694702},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47040849924087524},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4154886305332184},{"id":"https://openalex.org/C2554327","wikidata":"https://www.wikidata.org/wiki/Q2698599","display_name":"Coalescent theory","level":4,"score":0.41481342911720276},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34120726585388184},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32827746868133545},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22282153367996216},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19235825538635254},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.1646328866481781},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.13888803124427795},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.06740853190422058},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.06651830673217773},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C193252679","wikidata":"https://www.wikidata.org/wiki/Q242125","display_name":"Phylogenetic tree","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1142/s1793830920500147","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830920500147","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1811.11937","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.11937","pdf_url":"https://arxiv.org/pdf/1811.11937","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:2902236522","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1811.11937","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:scholarworks.boisestate.edu:math_facpubs-1251","is_oa":false,"landing_page_url":"https://scholarworks.boisestate.edu/math_facpubs/250","pdf_url":null,"source":{"id":"https://openalex.org/S4377196366","display_name":"Scholar Works  (Boise State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I120156002","host_organization_name":"Boise State University","host_organization_lineage":["https://openalex.org/I120156002"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications and Presentations","raw_type":"text"},{"id":"doi:10.48550/arxiv.1811.11937","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1811.11937","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":"pmh:oai:arXiv.org:1811.11937","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.11937","pdf_url":"https://arxiv.org/pdf/1811.11937","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G208183894","display_name":"REU site: Complexity Across Disciplines (CAD)","funder_award_id":"1359425","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2872101097","display_name":null,"funder_award_id":"DMS-1359425","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309625","display_name":"Boise State University","ror":"https://ror.org/02e3zdp86"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2902236522.pdf","grobid_xml":"https://content.openalex.org/works/W2902236522.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1502570864","https://openalex.org/W2004163905","https://openalex.org/W2011664512","https://openalex.org/W2046983574","https://openalex.org/W2063302961","https://openalex.org/W2065012512","https://openalex.org/W2085736516","https://openalex.org/W2149628296","https://openalex.org/W2964003467"],"related_works":["https://openalex.org/W2985697739","https://openalex.org/W3097045212","https://openalex.org/W2965325991","https://openalex.org/W1571904702","https://openalex.org/W2072229071","https://openalex.org/W34396323","https://openalex.org/W2007211528","https://openalex.org/W132656291","https://openalex.org/W2593657431","https://openalex.org/W3166755065","https://openalex.org/W2951186689","https://openalex.org/W2307544391","https://openalex.org/W2515185299","https://openalex.org/W2278556741","https://openalex.org/W2925661864","https://openalex.org/W1487122040","https://openalex.org/W3006907031","https://openalex.org/W2914770201","https://openalex.org/W2054075048","https://openalex.org/W2040539833"],"abstract_inverted_index":{"The":[0],"special":[1],"purpose":[2],"sorting":[3,16,32],"operation,":[4],"context":[5],"directed":[6],"swap":[7],"(CDS),":[8],"is":[9],"an":[10,127],"example":[11],"of":[12,41,44,51,81,91,111,133],"the":[13,37,48,56,89,109],"block":[14],"interchange":[15],"operation":[17],"studied":[18],"in":[19,36,93,113,124],"prior":[20],"work":[21],"on":[22],"permutation":[23],"sorting.":[24],"CDShas":[25],"been":[26],"postulated":[27],"to":[28,126],"model":[29],"certain":[30,131],"molecular":[31],"events":[33],"that":[34],"occur":[35],"genome":[38],"maintenance":[39],"program":[40],"some":[42],"species":[43],"ciliates.":[45],"We":[46],"investigate":[47],"mathematical":[49],"structure":[50],"permutations":[52,67,92,112],"not":[53],"sortable":[54],"by":[55],"CDSsorting":[57],"operation.":[58],"In":[59],"particular,":[60],"we":[61,104,137],"present":[62],"substantial":[63],"progress":[64],"towards":[65],"quantifying":[66],"with":[68,97,117],"a":[69,79,106],"given":[70],"strategic":[71,100,118],"pile":[72,119],"size,":[73],"which":[74,136],"can":[75],"be":[76],"understood":[77],"as":[78],"measure":[80],"CDSnon-sortability.":[82],"Our":[83],"main":[84],"results":[85],"include":[86],"formulas":[87],"for":[88,108,129],"number":[90,110],"[Formula:":[94,114,121],"see":[95,115,122],"text]":[96,116],"maximum":[98],"size":[99,120],"pile.":[101],"More":[102],"generally,":[103],"derive":[105],"formula":[107],"text],":[123],"addition":[125],"algorithm":[128],"computing":[130],"coefficients":[132],"this":[134],"formula,":[135],"call":[138],"merge":[139],"numbers.":[140]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}