Geodesic
Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted
The electronic journal of combinatorics, Tome 2 (1995)

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Zbl EuDML
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–Grassl algorithm and Stanley's $(P,\omega)$-partition theorem with the involution principle of Garsia and Milne.
DOI : 10.37236/1207
Classification : 05E10
Mots-clés : hook formulas, standard Young tableaux, Hillman-Grassl algorithm, involution principle 
C. Krattenthaler. Bijective proofs of the hook formulas for the number of standard Young tableaux, ordinary and shifted. The electronic journal of combinatorics, Tome 2 (1995). doi: 10.37236/1207
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     author = {C. Krattenthaler},
     title = {Bijective proofs of the hook formulas for the number of standard {Young} tableaux, ordinary and shifted},
     journal = {The electronic journal of combinatorics},
     year = {1995},
     volume = {2},
     doi = {10.37236/1207},
     zbl = {0822.05065},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1207/}
}
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