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After recalling the basic definitions, we present two inverse algorithms giving the desired bijection. The next part of the paper presents the proof of the bijectivity of our construction. The paper concludes with some examples."}},"publication_date":{"@media_type":"online","month":"01","day":"01","year":"1997"},"acceptance_date":{"@media_type":"online","month":"06","day":"09","year":"2015"},"publisher_item":{"item_number":{"@item_number_type":"article_number","value":"239"}},"program":[{"@name":"AccessIndicators","free_to_read":{"@start_date":"1997-01-01","value":""},"license_ref":[{"@applies_to":"am","@start_date":"1997-01-01","value":"https://about.hal.science/hal-authorisation-v1"},{"@applies_to":"vor","@start_date":"1997-01-01","value":"https://about.hal.science/hal-authorisation-v1"},{"@applies_to":"tdm","@start_date":"1997-01-01","value":"https://about.hal.science/hal-authorisation-v1"}]},{"related_item":{"intra_work_relation":{"@identifier-type":"uri","@relationship-type":"isSameAs","value":"https://hal.science/hal-00955690v1"}}}],"doi_data":{"doi":"10.46298/dmtcs.239","resource":"https://backiee.wasmer.app/https_dmtcs_episciences_org/239","collection":[{"@property":"crawler-based","item":{"@crawler":"iParadigms","resource":"https://hal.science/hal-00955690v1/document"}},{"@property":"text-mining","item":{"resource":{"@mime_type":"application/pdf","value":"https://hal.science/hal-00955690v1/document"}}}]},"keywords":{"en":["Hook-length formula","bijective proof","inverse algorithms"],"0":"[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]"}}},"database":{"current":{"mainPdfUrl":"https://hal.science/hal-00955690v1/document","original_language":"en","identifiers":{"permanent_item_number":239,"document_item_number":239,"repository_identifier":"hal-00955690","concept_identifier":null},"isTmp":false,"flag":"imported","type":{"title":"article"},"status":{"id":16,"label":{"en":"published","fr":"publié"}},"url":"https://backiee.wasmer.app/https_dmtcs_episciences_org/239","version":1,"files":{"link":"https://backiee.wasmer.app/https_dmtcs_episciences_org/239/pdf"},"dates":{"first_submission_date":"2015-03-26 16:17:03","posted_date":"2015-03-26 16:17:03","modification_date":"2025-03-31 21:02:50","publication_date":"1997-01-01 08:00:00"},"volume":{"id":68,"position":"75","number":null,"year":null,"has_proceedings":false,"titles":{"en":"Vol. 1"},"descriptions":null,"bibliographical_references":null,"settings":{"is_current_issue":false,"is_special_issue":false,"is_open":false}},"position_in_volume":3,"section":null,"journal":{"id":1,"code":"dmtcs","name":"Discrete Mathematics & Theoretical Computer Science","url":"https://backiee.wasmer.app/https_dmtcs_episciences_org"},"repository":{"id":"1","name":"HAL","type":"repository","status":"1","identifier":"oai:HAL:hal-00955690v1","base_url":"https://api.archives-ouvertes.fr/oai/hal/","doi_prefix":"","api_url":"https://api.archives-ouvertes.fr","doc_url":"https://hal.science/hal-00955690v1","paper_url":"https://hal.science/hal-00955690v1/document"},"cited_by":{"1123":{"id":"1123","citation":"{\"0\":{\"type\":null,\"author\":\"F. 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