Geodesic
Asymptotics of Young diagrams and hook numbers
The electronic journal of combinatorics, Tome 4 (1997) no. 1
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Asymptotic calculations are applied to study the degrees of certain sequences of characters of symmetric groups. Starting with a given partition $\mu$, we deduce several skew diagrams which are related to $\mu$. To each such skew diagram there corresponds the product of its hook numbers. By asymptotic methods we obtain some unexpected arithmetic properties between these products. The authors do not know "finite", nonasymptotic proofs of these results. The problem appeared in the study of the hook formula for various kinds of Young diagrams. The proofs are based on properties of shifted Schur functions, due to Okounkov and Olshanski. The theory of these functions arose from the asymptotic theory of Vershik and Kerov of the representations of the symmetric groups.
DOI : 10.37236/1307
Classification : 05E05
Mots-clés : characters of symmetric groups, partition, skew diagrams, hook numbers, Young diagrams, shifted Schur functions 
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     author = {Amitai Regev and Anatoly Vershik},
     title = {Asymptotics of {Young} diagrams and hook numbers},
     journal = {The electronic journal of combinatorics},
     year = {1997},
     volume = {4},
     number = {1},
     doi = {10.37236/1307},
     zbl = {0885.05109},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1307/}
}
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Amitai Regev; Anatoly Vershik. Asymptotics of Young diagrams and hook numbers. The electronic journal of combinatorics, Tome 4 (1997) no. 1. doi: 10.37236/1307

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