{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:22:24Z","timestamp":1759335744507,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Bijective proofs of the hook formulas for the number of ordinary standard Young tableaux and for the number of shifted standard Young tableaux are given. They are formulated in a uniform manner, and in fact prove $q$-analogues of the ordinary and shifted hook formulas. The proofs proceed by combining the ordinary, respectively shifted, Hillman\u2013Grassl algorithm and Stanley's $(P,\\omega)$-partition theorem with the involution principle of Garsia and Milne.<\/jats:p>","DOI":"10.37236\/1207","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:25:56Z","timestamp":1578705956000},"source":"Crossref","is-referenced-by-count":10,"title":["Bijective proofs of the hook formulas for the number of standard Young tableaux,  ordinary and shifted"],"prefix":"10.37236","volume":"2","author":[{"given":"C.","family":"Krattenthaler","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1995,7,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r13\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r13\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r13\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:31:37Z","timestamp":1579339897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,7,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1207","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,7,9]]},"article-number":"R13"}}