I'm learning about Young Tableaux.The number of standard Young tableaux of size n can can be generated by the recurrence relation:
$a(n)=a(n-1)+(n-1)a(n-2)$
By definition, A standard Young tableau (SYT) is a filling of a Young diagram
with the numbers 1, 2, . . . , n so that entries are increasing along
rows and columns.
Now I want to fill with n non-distinct numbers, how can I calculate the number of Young Tableaux again?I'm thinking about using Hook-Length formula, but It does not seem work out.
2026-02-22 21:24:57.1771795497
Standard Young Tableaux
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The count of all Semi-Standard Young Tableaux (SSYT) of size n and maximal element at most n is given in http://oeis.org/A209673. If you find a closed form expression for this, please let us know. The count of SSYT of shape $\lambda\vdash n$ is given by Stanley's Hook Content Formula. The pairs formed by all SSYT and all SYT of the same shape $\lambda\vdash n$ generate all $n^n$ different n-letter words of at most n different letters by the extended RSK-correspondance.