{"id":"https://openalex.org/W2004839796","doi":"https://doi.org/10.1016/s0304-3975(03)00223-8","title":"Some bijective results about the area of Schr\u00f6der paths","display_name":"Some bijective results about the area of Schr\u00f6der paths","publication_year":2003,"publication_date":"2003-05-01","ids":{"openalex":"https://openalex.org/W2004839796","doi":"https://doi.org/10.1016/s0304-3975(03)00223-8","mag":"2004839796"},"language":"en","primary_location":{"id":"doi:10.1016/s0304-3975(03)00223-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(03)00223-8","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017390053","display_name":"Luca Ferrari","orcid":"https://orcid.org/0000-0001-8096-6865"},"institutions":[{"id":"https://openalex.org/I4402554200","display_name":"Liceo scientifico statale Ulisse Dini","ror":"https://ror.org/006xg2x43","country_code":null,"type":"education","lineage":["https://openalex.org/I4402554200"]},{"id":"https://openalex.org/I45084792","display_name":"University of Florence","ror":"https://ror.org/04jr1s763","country_code":"IT","type":"education","lineage":["https://openalex.org/I45084792"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"L. Ferrari","raw_affiliation_strings":["Dipartimento di Matematica \u201cU. Dini\u201d, Viale Morgagni 67/A, 50134 Firenze, Italy","Dipartimento di Matematica U. Dini, Viale Morgagni 67/A, 50134 Firenze, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cU. Dini\u201d, Viale Morgagni 67/A, 50134 Firenze, Italy","institution_ids":["https://openalex.org/I45084792","https://openalex.org/I4402554200"]},{"raw_affiliation_string":"Dipartimento di Matematica U. Dini, Viale Morgagni 67/A, 50134 Firenze, Italy#TAB#","institution_ids":["https://openalex.org/I4402554200"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013519924","display_name":"Elisabetta Grazzini","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108802","display_name":"Gestione Sistemi per l\u2019Informatica (Italy)","ror":"https://ror.org/01gyw2394","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210108802"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. Grazzini","raw_affiliation_strings":["Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy","Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy","institution_ids":["https://openalex.org/I4210108802"]},{"raw_affiliation_string":"Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy#TAB#","institution_ids":["https://openalex.org/I4210108802"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107701414","display_name":"Elisa Pergola","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108802","display_name":"Gestione Sistemi per l\u2019Informatica (Italy)","ror":"https://ror.org/01gyw2394","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210108802"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. Pergola","raw_affiliation_strings":["Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy","Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy","institution_ids":["https://openalex.org/I4210108802"]},{"raw_affiliation_string":"Dipartimento di Sistemi e Informatica, via Lombroso 6/17, 50134 Firenze, Italy#TAB#","institution_ids":["https://openalex.org/I4210108802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018231504","display_name":"Simone Rinaldi","orcid":null},"institutions":[{"id":"https://openalex.org/I102064193","display_name":"University of Siena","ror":"https://ror.org/01tevnk56","country_code":"IT","type":"education","lineage":["https://openalex.org/I102064193"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"S. Rinaldi","raw_affiliation_strings":["Dipartimento di Matematica \u201cR. Magari\u201d, via del Capitano 15, 53100 Siena, Italy","Dipartimento di Matematica R. Magari, via del Capitano 15, 53100 Siena, Italy#TAB#"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u201cR. Magari\u201d, via del Capitano 15, 53100 Siena, Italy","institution_ids":["https://openalex.org/I102064193"]},{"raw_affiliation_string":"Dipartimento di Matematica R. Magari, via del Capitano 15, 53100 Siena, Italy#TAB#","institution_ids":["https://openalex.org/I102064193"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5017390053"],"corresponding_institution_ids":["https://openalex.org/I4402554200","https://openalex.org/I45084792"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":0.5526,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60132383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"307","issue":"2","first_page":"327","last_page":"335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.9926000237464905,"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":0.8046326637268066},{"id":"https://openalex.org/keywords/encyclopedia","display_name":"Encyclopedia","score":0.7034434080123901},{"id":"https://openalex.org/keywords/integer-sequence","display_name":"Integer sequence","score":0.6944655776023865},{"id":"https://openalex.org/keywords/longest-common-subsequence-problem","display_name":"Longest common subsequence problem","score":0.6669826507568359},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6528074741363525},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.6422078609466553},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6054093241691589},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.6030924916267395},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5973659157752991},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.5417467355728149},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5408838391304016},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4015622138977051},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26156169176101685},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.24446728825569153},{"id":"https://openalex.org/keywords/library-science","display_name":"Library science","score":0.05674952268600464}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.8046326637268066},{"id":"https://openalex.org/C148863701","wikidata":"https://www.wikidata.org/wiki/Q5292","display_name":"Encyclopedia","level":2,"score":0.7034434080123901},{"id":"https://openalex.org/C61994974","wikidata":"https://www.wikidata.org/wiki/Q2297602","display_name":"Integer sequence","level":3,"score":0.6944655776023865},{"id":"https://openalex.org/C120098539","wikidata":"https://www.wikidata.org/wiki/Q141001","display_name":"Longest common subsequence problem","level":2,"score":0.6669826507568359},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6528074741363525},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.6422078609466553},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6054093241691589},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.6030924916267395},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5973659157752991},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.5417467355728149},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5408838391304016},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4015622138977051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26156169176101685},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.24446728825569153},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.05674952268600464},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1016/s0304-3975(03)00223-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0304-3975(03)00223-8","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/309906","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/309906","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:usiena-air.unisi.it:11365/10559","is_oa":false,"landing_page_url":"http://hdl.handle.net/11365/10559","pdf_url":null,"source":{"id":"https://openalex.org/S4377196319","display_name":"Use Siena air (University of Siena)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102064193","host_organization_name":"University of Siena","host_organization_lineage":["https://openalex.org/I102064193"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W128678661","https://openalex.org/W1551177513","https://openalex.org/W2017807608","https://openalex.org/W2044758476","https://openalex.org/W2046479912","https://openalex.org/W2062984219","https://openalex.org/W2126209209","https://openalex.org/W2134733540","https://openalex.org/W2914659449","https://openalex.org/W6605197704"],"related_works":["https://openalex.org/W1540010783","https://openalex.org/W3022573534","https://openalex.org/W1746697883","https://openalex.org/W4225868058","https://openalex.org/W4389489786","https://openalex.org/W4289596129","https://openalex.org/W2969919693","https://openalex.org/W3083981518","https://openalex.org/W4323338832","https://openalex.org/W3094761360"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
