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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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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 
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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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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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