{"id":"https://openalex.org/W1779791987","doi":"https://doi.org/10.37236/4768","title":"A Relationship Between Generalized Davenport-Schinzel Sequences and Interval Chains","display_name":"A Relationship Between Generalized Davenport-Schinzel Sequences and Interval Chains","publication_year":2015,"publication_date":"2015-08-14","ids":{"openalex":"https://openalex.org/W1779791987","doi":"https://doi.org/10.37236/4768","mag":"1779791987"},"language":"en","primary_location":{"id":"doi:10.37236/4768","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4768","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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/4768","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016568974","display_name":"Jesse Geneson","orcid":"https://orcid.org/0000-0001-7148-5947"},"institutions":[{"id":"https://openalex.org/I4210109586","display_name":"Moscow Institute of Thermal Technology","ror":"https://ror.org/021es5e59","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210109586"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Jesse Geneson","raw_affiliation_strings":["MIT"],"affiliations":[{"raw_affiliation_string":"MIT","institution_ids":["https://openalex.org/I4210109586"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5016568974"],"corresponding_institution_ids":["https://openalex.org/I4210109586"],"apc_list":null,"apc_paid":null,"fwci":0.6014,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.71875777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"22","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9986000061035156,"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/T11567","display_name":"semigroups and automata theory","score":0.9986000061035156,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/subsequence","display_name":"Subsequence","score":0.8990343809127808},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8961334228515625},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8256386518478394},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7069823145866394},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6861099004745483},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.6545215249061584},{"id":"https://openalex.org/keywords/concatenation","display_name":"Concatenation (mathematics)","score":0.5961505174636841},{"id":"https://openalex.org/keywords/tuple","display_name":"Tuple","score":0.5354374051094055},{"id":"https://openalex.org/keywords/alternation","display_name":"Alternation (linguistics)","score":0.5191844701766968},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.49816036224365234},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4468558132648468},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3787487745285034},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060368865728378296}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.8990343809127808},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8961334228515625},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256386518478394},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7069823145866394},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6861099004745483},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.6545215249061584},{"id":"https://openalex.org/C87619178","wikidata":"https://www.wikidata.org/wiki/Q126002","display_name":"Concatenation (mathematics)","level":2,"score":0.5961505174636841},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.5354374051094055},{"id":"https://openalex.org/C26826806","wikidata":"https://www.wikidata.org/wiki/Q438358","display_name":"Alternation (linguistics)","level":2,"score":0.5191844701766968},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.49816036224365234},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4468558132648468},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3787487745285034},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060368865728378296},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4768","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4768","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:dspace.mit.edu:1721.1/100752","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/100752","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"European Mathematical Information Service (EMIS)","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"doi:10.37236/4768","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4768","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1705251487","https://openalex.org/W1768195728","https://openalex.org/W1979382580","https://openalex.org/W1998230386","https://openalex.org/W2002729962","https://openalex.org/W2011451001","https://openalex.org/W2019176509","https://openalex.org/W2025410851","https://openalex.org/W2028747718","https://openalex.org/W2072233942","https://openalex.org/W2246233041","https://openalex.org/W2320799707","https://openalex.org/W2730912875","https://openalex.org/W2963302403","https://openalex.org/W3148691794"],"related_works":["https://openalex.org/W2373577936","https://openalex.org/W4221148444","https://openalex.org/W4387678054","https://openalex.org/W2389596151","https://openalex.org/W3095575180","https://openalex.org/W4306784355","https://openalex.org/W4230102134","https://openalex.org/W2169308097","https://openalex.org/W2132777284","https://openalex.org/W1999473833"],"abstract_inverted_index":{"Let":[0],"an":[1,66,78,224],"$(r,":[2,145],"s)$-formation":[3],"be":[4,21,194,206],"a":[5,16,19,22,34,69,89,166],"concatenation":[6],"of":[7,10,18,24,36,42,71,84,92,133,165,169,185,198,216,226],"$s$":[8,72],"permutations":[9],"$r$":[11,183],"distinct":[12,26,73,134,199],"letters,":[13],"and":[14,65,106,121,219,278],"let":[15],"block":[17],"sequence":[20,35,138,203],"subsequence":[23,222],"consecutive":[25],"letters.":[27],"A":[28],"$k$-chain":[29],"on":[30,140,174],"$[1,":[31,175],"m]$":[32,176],"is":[33,68,87,158],"$k$":[37,214],"consecutive,":[38],"disjoint,":[39],"nonempty":[40],"intervals":[41],"the":[43,85,93,113,130,159,162,190,195],"form":[44],"$[a_{0},":[45],"a_{1}]":[46],"[a_{1}+1,":[47],"a_{2}]":[48],"\\ldots":[49,60],"[a_{k-1}+1,":[50],"a_{k}]$":[51],"for":[52,103,116,239,257,284],"integers":[53],"$1":[54,122],"\\leq":[55,57,63,123,125,127],"a_{0}":[56],"a_{1}":[58],"<":[59,61],"a_{k}":[62],"m$,":[64],"$s$-tuple":[67,76,86],"set":[70],"integers.":[74],"An":[75],"stabs":[77],"interval":[79,91,104],"chain":[80],"if":[81],"each":[82],"element":[83],"in":[88,136,151,201],"different":[90],"chain.":[94],"Alon":[95],"et":[96],"al.":[97],"(2008)":[98],"observed":[99],"similarities":[100],"between":[101],"bounds":[102,267],"chains":[105],"Davenport-Schinzel":[107],"sequences,":[108],"but":[109],"did":[110],"not":[111,181],"identify":[112],"cause.We":[114],"show":[115,246],"all":[117,187,240,258,285],"$r":[118],"\\geq":[119,243,260,288],"1$":[120],"s":[124],"k":[126],"m$":[128],"that":[129,148,178,232,247,270],"maximum":[131,163,196],"number":[132,197],"letters":[135,200],"any":[137,202],"$S$":[139,152],"$m+1$":[141],"blocks":[142],"avoiding":[143],"every":[144,149,217],"s+1)$-formation":[146],"such":[147],"letter":[150],"occurs":[153],"at":[154,212],"least":[155,213],"$k+1$":[156],"times":[157],"same":[160,191],"as":[161],"size":[164],"collection":[167],"$X$":[168,186],"(not":[170],"necessarily":[171],"distinct)":[172],"$k$-chains":[173],"so":[177],"there":[179],"do":[180],"exist":[182],"elements":[184],"stabbed":[188],"by":[189],"$s$-tuple.Let":[192],"$D_{s,k}(m)$":[193],"which":[204,268],"can":[205],"partitioned":[207],"into":[208],"$m$":[209],"blocks,":[210],"has":[211,220],"occurrences":[215],"letter,":[218],"no":[221],"forming":[223],"alternation":[225],"length":[227],"$s$.":[228],"Nivasch":[229],"(2010)":[230],"proved":[231],"$D_{5,":[233,271,279],"2d+1}(m)":[234],"=":[235,250,273,281],"\\Theta(":[236],"m":[237],"\\alpha_{d}(m))$":[238,283],"fixed":[241,286],"$d":[242,287],"2$.":[244,261],"We":[245,262],"$D_{s+1,":[248],"s}(m)":[249],"\\binom{m-":[251],"\\lceil":[252],"\\frac{s}{2}":[253,255],"\\rceil}{\\lfloor":[254],"\\rfloor}$":[256],"$s":[259],"also":[263],"prove":[264],"new":[265],"lower":[266],"imply":[269],"6}(m)":[272],"\\Theta(m":[274,282],"\\log":[275,276],"m)$":[277],"2d+2}(m)":[280],"3$.":[289]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}