{"id":"https://openalex.org/W1486301413","doi":"https://doi.org/10.37236/1505","title":"Bijections for hook pair identities","display_name":"Bijections for hook pair identities","publication_year":2000,"publication_date":"2000-04-10","ids":{"openalex":"https://openalex.org/W1486301413","doi":"https://doi.org/10.37236/1505","mag":"1486301413"},"language":"en","primary_location":{"id":"doi:10.37236/1505","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1505","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r27/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r27/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040427357","display_name":"Christian Krattenthaler","orcid":"https://orcid.org/0000-0001-6930-0253"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"C. Krattenthaler","raw_affiliation_strings":["Institut fr Mathematik der Universitt Wien, Strudlhofgasse 4, A-1090 Wien, Austria","Institut f\u00fcr Mathematik der Universit\u00e4t Wien, Strudlhofgasse 4, A-1090 Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Institut fr Mathematik der Universitt Wien, Strudlhofgasse 4, A-1090 Wien, Austria","institution_ids":[]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik der Universit\u00e4t Wien, Strudlhofgasse 4, A-1090 Wien, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040427357"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":1.9958,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.81613508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"7","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9930999875068665,"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":0.9930999875068665,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9909999966621399,"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/T12504","display_name":"Mathematics and Applications","score":0.9549999833106995,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bijection-injection-and-surjection","display_name":"Bijection, injection and surjection","score":0.9807670712471008},{"id":"https://openalex.org/keywords/hook","display_name":"Hook","score":0.9629961252212524},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8957024812698364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8165686130523682},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7527716159820557},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6984254717826843},{"id":"https://openalex.org/keywords/polyomino","display_name":"Polyomino","score":0.4791088104248047},{"id":"https://openalex.org/keywords/combinatorial-proof","display_name":"Combinatorial proof","score":0.4252206087112427},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11530396342277527}],"concepts":[{"id":"https://openalex.org/C48659774","wikidata":"https://www.wikidata.org/wiki/Q4907197","display_name":"Bijection, injection and surjection","level":3,"score":0.9807670712471008},{"id":"https://openalex.org/C2777586403","wikidata":"https://www.wikidata.org/wiki/Q4243098","display_name":"Hook","level":2,"score":0.9629961252212524},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8957024812698364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8165686130523682},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7527716159820557},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6984254717826843},{"id":"https://openalex.org/C69919132","wikidata":"https://www.wikidata.org/wiki/Q1144819","display_name":"Polyomino","level":3,"score":0.4791088104248047},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.4252206087112427},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11530396342277527},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/1505","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1505","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r27/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":false,"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:10.1.1.11.8859","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.8859","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathe2.uni-bayreuth.de/axel/papers/./krattenthaler:bijections_for_hook_pair_identities.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.4559","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.4559","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.univie.ac.at/EMIS/journals/EJC/Volume_7/PDF/v7i1r27.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.24.5499","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.24.5499","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.univie.ac.at/EMIS/journals/EJC/Volume_7/PostScriptfiles/v7i1r27.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.241.6001","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.241.6001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/9912096v1.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1505","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1505","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v7i1r27/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":false,"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/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1486301413.pdf","grobid_xml":"https://content.openalex.org/works/W1486301413.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1971345196","https://openalex.org/W2000510453","https://openalex.org/W2042080846","https://openalex.org/W2050706595","https://openalex.org/W2096053482","https://openalex.org/W2103597166","https://openalex.org/W2134984950","https://openalex.org/W4300302225"],"related_works":["https://openalex.org/W2952259524","https://openalex.org/W2160566290","https://openalex.org/W1626053433","https://openalex.org/W2806276129","https://openalex.org/W4299611798","https://openalex.org/W2963449060","https://openalex.org/W2027759271","https://openalex.org/W3083163437","https://openalex.org/W4286421839","https://openalex.org/W1525032898"],"abstract_inverted_index":{"Short,":[0],"bijective":[1],"proofs":[2],"of":[3,7,12,15],"identities":[4,23],"for":[5],"multisets":[6],"'hook":[8],"pairs'":[9],"(arm-leg":[10],"pairs)":[11],"the":[13],"cells":[14],"certain":[16],"diagrams":[17],"are":[18],"given.":[19],"These":[20],"hook":[21],"pair":[22],"were":[24],"originally":[25],"found":[26],"by":[27],"Regev.":[28]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
