{"id":"https://openalex.org/W4214595959","doi":"https://doi.org/10.1007/s00453-022-00939-7","title":"Tree Automata and Pigeonhole Classes of Matroids: I","display_name":"Tree Automata and Pigeonhole Classes of Matroids: I","publication_year":2022,"publication_date":"2022-02-23","ids":{"openalex":"https://openalex.org/W4214595959","doi":"https://doi.org/10.1007/s00453-022-00939-7"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00939-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00939-7.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00939-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021037221","display_name":"Daryl Funk","orcid":"https://orcid.org/0000-0003-0421-0059"},"institutions":[{"id":"https://openalex.org/I177567560","display_name":"Douglas College","ror":"https://ror.org/03wze7d53","country_code":"CA","type":"education","lineage":["https://openalex.org/I177567560"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Daryl Funk","raw_affiliation_strings":["Department of Mathematics, Douglas College, Vancouver, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Douglas College, Vancouver, Canada","institution_ids":["https://openalex.org/I177567560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050651276","display_name":"Dillon Mayhew","orcid":"https://orcid.org/0000-0003-4086-0980"},"institutions":[{"id":"https://openalex.org/I41156924","display_name":"Victoria University of Wellington","ror":"https://ror.org/0040r6f76","country_code":"NZ","type":"funder","lineage":["https://openalex.org/I41156924"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Dillon Mayhew","raw_affiliation_strings":["School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Victoria University of Wellington, Wellington, New Zealand","institution_ids":["https://openalex.org/I41156924"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068304065","display_name":"Mike Newman","orcid":null},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"funder","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mike Newman","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada","institution_ids":["https://openalex.org/I153718931"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050651276"],"corresponding_institution_ids":["https://openalex.org/I41156924"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.181,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":1,"citation_normalized_percentile":{"value":0.35195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":59,"max":69},"biblio":{"volume":"84","issue":"7","first_page":"1795","last_page":"1834"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9994,"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"}},"topics":[{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9994,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9972,"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/pigeonhole-principle","display_name":"Pigeonhole principle","score":0.7920473},{"id":"https://openalex.org/keywords/oriented-matroid","display_name":"Oriented matroid","score":0.46601915},{"id":"https://openalex.org/keywords/tree-automaton","display_name":"Tree automaton","score":0.45190093},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.43764254}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.92898154},{"id":"https://openalex.org/C171988527","wikidata":"https://www.wikidata.org/wiki/Q188276","display_name":"Pigeonhole principle","level":2,"score":0.7920473},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6272703},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6054571},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6020447},{"id":"https://openalex.org/C111034964","wikidata":"https://www.wikidata.org/wiki/Q5597156","display_name":"Graphic matroid","level":3,"score":0.57471484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.51329273},{"id":"https://openalex.org/C178621168","wikidata":"https://www.wikidata.org/wiki/Q16155113","display_name":"Oriented matroid","level":4,"score":0.46601915},{"id":"https://openalex.org/C2778583254","wikidata":"https://www.wikidata.org/wiki/Q2872598","display_name":"Tree automaton","level":3,"score":0.45190093},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.43764254},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4367473},{"id":"https://openalex.org/C22425182","wikidata":"https://www.wikidata.org/wiki/Q6787906","display_name":"Matroid partitioning","level":4,"score":0.42352346},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24674565},{"id":"https://openalex.org/C112505250","wikidata":"https://www.wikidata.org/wiki/Q787116","display_name":"Automaton","level":2,"score":0.21380392},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.098582804},{"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":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00939-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00939-7.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-022-00939-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-022-00939-7.pdf","source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319965","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Springer Nature","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[{"funder":"https://openalex.org/F4320320802","funder_display_name":"Victoria University of Wellington","award_id":null}],"datasets":[],"versions":[],"referenced_works_count":21,"referenced_works":["https://openalex.org/W1489366126","https://openalex.org/W1570445666","https://openalex.org/W1602589099","https://openalex.org/W1964291804","https://openalex.org/W1966617477","https://openalex.org/W1980469100","https://openalex.org/W1999958048","https://openalex.org/W2000941444","https://openalex.org/W2014803743","https://openalex.org/W2020927880","https://openalex.org/W2028357390","https://openalex.org/W2029001691","https://openalex.org/W2054801208","https://openalex.org/W2063951771","https://openalex.org/W2079618965","https://openalex.org/W2116087731","https://openalex.org/W2963139101","https://openalex.org/W2963193004","https://openalex.org/W3146773416","https://openalex.org/W4231868828","https://openalex.org/W4292230561"],"related_works":["https://openalex.org/W4303709689","https://openalex.org/W2980228156","https://openalex.org/W2625145881","https://openalex.org/W2400862597","https://openalex.org/W2378157773","https://openalex.org/W2153065381","https://openalex.org/W2072414647","https://openalex.org/W2058489697","https://openalex.org/W1984819493","https://openalex.org/W1978795414"],"abstract_inverted_index":{"Abstract":[0],"Hlin\u011bn\u00fd\u2019s":[1,131,149],"Theorem":[2,132,150],"shows":[3],"that":[4,68,130,187,213],"any":[5,135,174,232],"sentence":[6],"in":[7,17,54,64,227],"the":[8,21,80,87,105,125,152,183,220],"monadic":[9,228,240],"second-order":[10,229,241],"logic":[11],"of":[12,28,73,92,124,154,182,185,217],"matroids":[13,36,218],"can":[14,57,188,224],"be":[15,58,189,225],"tested":[16],"polynomial":[18],"time,":[19],"when":[20],"input":[22],"is":[23,47,107,173,196],"limited":[24],"to":[25,134,147,151],"a":[26,48,55,61,66,70,114,140,180,194,199,215,238],"class":[27,56,81,106,112,216],"$${\\mathbb":[29,41],"{F}}$$":[30,42],"":[32,44,166],"F":[33,45],"":[34,46,168],"-representable":[35],"with":[37,97,234],"bounded":[38,71,83,98,102,208,235],"branch-width":[39,99,236],"(where":[40],"finite":[49,175],"field).":[50],"If":[51],"each":[52],"matroid":[53],"decomposed":[59],"by":[60,198],"subcubic":[62],"tree":[63,192,200],"such":[65],"way":[67],"only":[69,204],"amount":[72],"information":[74],"flows":[75],"across":[76],"displayed":[77],"separations,":[78],"then":[79,104,231],"has":[82,101,113,207,219,237],"decomposition-width.":[84,209],"We":[85,128,177],"introduce":[86],"pigeonhole":[88,111,137,221],"property":[89],"for":[90],"classes":[91,153],"matroids:":[93],"if":[94,202,205,214],"every":[95],"subclass":[96,233],"also":[100,178],"decomposition-width,":[103],"pigeonhole.":[108],"An":[109],"efficiently":[110,136],"stronger":[115],"property,":[116,222],"involving":[117],"an":[118],"efficiently-computable":[119],"equivalence":[120],"relation":[121],"on":[122],"subsets":[123],"ground":[126],"set.":[127],"show":[129,212],"extends":[133],"class.":[138],"In":[139],"sequel":[141],"paper,":[142],"we":[143,211],"use":[144],"these":[145],"ideas":[146],"extend":[148],"fundamental":[155],"transversal":[156],"matroids,":[157,160,162,170],"lattice":[158],"path":[159],"bicircular":[161],"and":[163,203,223],"$$H$$":[164],"H":[167],"-gain-graphic":[169],"where":[171],"H":[172],"group.":[176],"give":[179],"characterisation":[181],"families":[184],"hypergraphs":[186],"described":[190],"via":[191],"automata:":[193],"family":[195],"defined":[197,226],"automaton":[201],"it":[206],"Furthermore,":[210],"logic,":[230],"decidable":[239],"theory.":[242]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4214595959","counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-03-24T04:12:40.890272","created_date":"2022-03-02"}